The story...

The WTC was designed to withstand the impact of a 707. There's very little difference between the 707 and the 767, therefore why should the 9/11 impacts have caused the towers to fall?

Our take...

You can see this argument spelled out in a commentary on the FEMA 911 report at 911Research. For example, here's one part of FEMA's explanation...

The WTC towers were the first structures outside of the military and the nuclear industries whose design considered the impact of a jet airliner, the Boeing 707. It was assumed in the 1960s design analysis for the WTC towers that an aircraft, lost in fog and seeking to land at a nearby airport, like the B-25 Mitchell bomber that struck the Empire State Building on July 28, 1945, might strike a WTC tower while low on fuel and at landing speeds.
http://911research.wtc7.net/mirrors/guardian/WTC/WTC_ch1.htm

And the response:

That the WTC was designed only to withstand a collision with a Boeing 707 that was seeking to land at a nearby airport, and therefore low on fuel, is an obvious lie. Why is it an obvious lie? Well, because if you take into consideration planes that are landing at an airport, then you must consider planes that are taking off, and such planes are fully laden with fuel.
http://911research.wtc7.net/mirrors/guardian/WTC/WTC_ch1.htm

The FEMA details:

The Boeing 707 that was considered in the design of the towers was estimated to have a gross weight of 263,000 pounds and a flight speed of 180 mph as it approached an airport; the Boeing 767-200ER aircraft that were used to attack the towers had an estimated gross weight of 274,000 pounds and flight speeds of 470 to 590 mph upon impact.
http://911research.wtc7.net/mirrors/guardian/WTC/WTC_ch1.htm

The 707 weight here is the subject of some controversy. It is close to the weight of a 707-120, perhaps a 707-220 (http://www.aviation-history.com/boeing/707.html), but others say FEMA should be quoting the weight of a 320-B. That would something be in the range of 295,000 to 326,000 pounds, making it heavier than the 767-200ER craft used on 9/11.

Anyway, the response:

What evidence do we have that the designers only considered impacts by planes that were flying close to stall speed (the stall speed, is the speed below which the aircraft falls out of the sky). Apparently, we only have this articles word for it. And we already know that they are quite willing to lie and exaggerate the facts.
http://911research.wtc7.net/mirrors/guardian/WTC/WTC_ch1.htm

(The commentary runs throughout the report, so follow the original link to read it if you want to see if the "lie and exaggerate the facts" comment is true).

One initial answer to this came from Leslie Robertson, lead structural engineer of the WTC. According to his account the assumption was that the collision would be with a relatively slow-moving 707, lost in fog:

The two towers were the first structures outside of the military and nuclear industries designed to resist the impact of a jet airliner, the Boeing 707. It was assumed that the jetliner would be lost in the fog, seeking to land at JFK or at Newark.
http://www.nae.edu/nae/bridgecom.nsf/weblinks/CGOZ-58NLCB?OpenDocument

The full document includes a graphic indicating the 707 impact speed was indeed estimated to be 290 km/h (around 180 mph), which compares with “flight speeds of 470 to 590 mph upon impact” for the 9/11 attacks.

This account later appeared to be contradicted by NIST, however...

The investigators also said that newly disclosed Port Authority documents suggested that the towers were designed to withstand the kind of airplane strike that they suffered on Sept. 11.

Earlier statements by Port Authority officials and outside engineers involved in designing the buildings suggested that the designers considered an accidental crash only by slower aircraft, moving at less than 200 miles per hour. The newly disclosed documents, from the 1960's, show that the Port Authority considered aircraft moving at 600 m.p.h., slightly faster and therefore more destructive than the ones that did hit the towers, Dr. Sunder said.
http://www.nytimes.com/2003/12/03/nyregion/03TOWE.html?ei=5007&en=a2c62eb2b42cf30c&ex=1385874000&adxnnl=1

The level of disagreement between the Port Authority and Robertson on this point is revealed in a further article.

Robertson took the time to calculate how well his towers would handle the impact from a Boeing 707, the largest jetliner in service at the time. He says that his calculations assumed a plane lost in a fog while searching for an airport at relatively low speed, like the B-25 bomber. He concluded that the towers would remain standing despite the force of the impact and the hole it would punch out. The new technologies he had installed after the motion experiments and wind-tunnel work had created a structure more than strong enough to withstand such a blow.

Exactly how Robertson performed these calculations is apparently lost -- he says he cannot find a copy of the report. Several engineers who worked with him at the time, including the director of his computer department, say they have no recollection of ever seeing the study. But the Port Authority, eager to mount a counterattack against Wien, seized on the results -- and may in fact have exaggerated them. One architect working for the Port Authority issued a statement to the press, covered in a prominent article in The Times, explaining that Robertson's study proved that the towers could withstand the impact of a jetliner moving at 600 miles an hour. That was perhaps three times the speed that Robertson had considered. If Robertson saw the article in the paper, he never spoke up about the discrepancy. No one else issued a correction, and the question was answered in many people's minds: the towers were as safe as could be expected, even in the most cataclysmic of circumstances.

There were only two problems. The first, of course, was that no study of the impact of a 600-mile-an-hour plane ever existed. ''That's got nothing to do with the reality of what we did,'' Robertson snapped when shown the Port Authority architect's statement more than three decades later. The second problem was that no one thought to take into account the fires that would inevitably break out when the jetliner's fuel exploded, exactly as the B-25's had. And if Wien was the trade center's Cassandra, fire protection would become its Achilles' heel.
http://scott-juris.blogspot.com/The%20Height%20of%20Ambition%20Part%20Four.pdf

Note that according to this, the towers were not specifically designed to survive the impact from a plane. Rather, Robertson carried out some calculations on the existing design to assess what the results of impact might be.

Further, whatever the truth about the speed of the plane, there’s no indication that the design considered the effects of the fire. Leslie Robertson says the towers were not designed to handle it:.

To the best of our knowledge, little was known about the effects of a fire from such an aircraft, and no designs were prepared for that circumstance. Indeed, at that time, no fireproofing systems were available to control the effects of such fires.
http://www.nae.edu/nae/bridgecom.nsf/weblinks/CGOZ-58NLCB?OpenDocument

And even the later documents reported by NIST apparently left the issue open to question.

Potentially challenging other statements by Port Authority engineers, Dr. Sunder said it was now uncertain whether the authority fully considered the fuel and its effects when it studied the towers' safety during the design phase.

"Whether the fuel was taken into account or not is an open question," Dr. Sunder said
http://www.nytimes.com/2003/12/03/nyregion/03TOWE.html?ei=5007&en=a2c62eb2b42cf30c&ex=1385874000&adxnnl=1

And of course this matters, because the towers did withstand the impact: it’s claimed that the combination of that damage and the resulting fires is what brought them down.
What is clear from Robertson, at least, is that he believes the "robustness of the towers was exemplary", and that "the fact that the structures stood long enough for tens of thousands to escape is a tribute to the many talented men and women who spent endless hours toiling over the design and construction of the project". That is, he appears to be saying the towers performed better than expected, not worse.