The collection box wasn't missed, but since it was probably in an area that has a population not yet Americanized and used to using the mail to pay their bills, there weren't many letters in it.
The carrier put all the letters in a flat tray (a normal practice), and placed it in the back of his collection vehicle.
At the next stop, in a busier area, with a heavily American or Americanized population, the flat tray had already been placed in the collection box, so the carrier pulled it out and placed it right on top of the mail in the other flat tray.
Once the mail was swept from the "top" tray, the clerk thought she had two empty trays and simply set them aside, as normal.
It was only later on when those trays were given to a mailer for what is now the heaviest mailing season of the year that the envelopes were discovered. The mailer's people simply tossed the letters (bearing stamps) in with their own First Class corporate mail going to the Post Office.
Odds are those people were exposed to the anthrax attack. So was the carrier, and he might only now be showing any symptoms.
The conclusion is that the anthrax letters were mailed BEFORE 9/11, but they are being delivered only now because they were found in supposedly empty equipment. The USPS has a standard notice for that situation, which does happen from time to time.
And, here's another thought - the pieces were actually mailed in a different city, e.g. Springfield Virginia by local Arab terrorists known to have visited/lived there. Again, they got caught up in the empty tray business, but this time empty Northern Virginia SCF trays were sent to Trenton where they have a much heavier originating mail volume this time of year.
Other scenarios are possible.