"The SSDI Social Security Death Index, the registry of all US Social Security numbers belonging to deceased persons, is a guide to who has really died (ssdi.genealogy.rootsweb.com). Not many of the supposedly-dead passengers turn up on this index. Flight AA11 which supposedly crashed into the North tower, had a flight crew of eleven according to published lists, including pilot John Ogonowski and flight attendants Betty Ong and Madeleine Sweeney. The SSDI list cites only one of these eleven persons as having died on that day".
This sounds impressive, until you actually visit the SSDI and look at the warnings about its data. These are spread across several pages.
Common Misconceptions About The SSDI
The Social Security Death Master File contains records of everyone who has died in the United States.
NO. Because this data was produced by the Social Security Administration, the database only concerns itself with those individuals who were involved with the Social Security program. Those who did not have cards are not in the file.
The Social Security Death Master File contains death records for everyone who possessed a Social Security card while living.
NO. Individuals were added to the file as their deaths were reported to the Administration. This often occurred when family members applied for a lump sum benefit at death. If the SSA was not informed of a person's death, then they are not on file, whether they had a Social Security Card or not.
Another page explains other reasons as to "Why You May Not Find Your Ancestors":
The individual did not have a Social Security card. Especially before 1951, it is entirely possible that your ancestor did not have a Social Security number at all. The self-employed, farmers, military, government employees, some professional groups (doctors, lawyers), did not receive coverage until the 1950s and 60s. Certain members of the family may have never had the need to enroll in Social Security (retired individuals, housewives, etc.).
The individual had a Social Security card, but his/her death was not reported to the SSA. The Death Master File only contains those deaths reported to the SSA.
The individual is in the file, but listed under another name or another spelling. Try other spellings of the individual's name, including middle names, nicknames, initials, maiden names, other married surnames, etc.
The individual is in the file, but original data was reported or recorded incorrectly.
The SSDI does not include death records for everyone who has been issued a Social Security Number (card). Common reasons for exclusion include the following:
The death was not reported to the Social Security Administration (SSA).
The death occurred before the Death Master File was maintained in a computer database. About 98 percent of the deaths in this database occurred between 1962 and the present.
The person did not participate in the Social Security program.
Survivor death benefits were (are) being paid to dependents or spouse.
A recent death may not be indexed yet.
Human error. (Before you give up, read the section titled "Missing Entries in the SSDI.")
Reasons you might not find someone in the SSDI
Prior to the 1960s, farmers, housewives, government employees, non-employed individuals, and those with a separate retirement plan might not have had a Social Security number. It was not until 1988 that all children had to have Social Security numbers.
It's very clear that this is not an exhaustive or complete database. It may be true that fewer relatives than usual reported the deaths to the SSA, but then these weren't ordinary deaths. Is it really so surprising that the paperwork wasn't completed in all cases? Compensation was available from elsewhere, so there would be less likelihood of applying for death benefits. And as Ancestry.com points out, "many funeral directors will notify the SSA as a service to families of the deceased" (http://www.ancestry.com/search/rectype/vital/ssdi/miscon.htm), but if you don't have a funeral then it'll only happen if you remember to do it yourself.