After some discussion and me examining TotalVac's web site and my original order invoice, I could only conclude that they had shipped me the wrong part, for a different model of DustBuster. I wrote their returns-authorization address giving my order number the part number I ordered (and confirming the dimensions of the old bag on my father-in-law's Dustbuster), and giving the dimensions and shape (trapezoidal instead of rectangular) and my speculation that they'd shipped me the wrong part. I then sat back expecting to be told, at best, that I'd have to ship the part back to them, possibly having to spend more than the $4 cost of the part in the first place.
I've received an e-mail from them apologizing for the mis-pick, promising to ship us a new one when they get a new shipment (they're out of stock right now), and telling us not to bother shipping the wrong part back to them.
It's nice when you get sensible customer service. They realized that it would almost certainly cost them as much to re-acquire the part as the part cost them to buy in the first place, and therefore wrote it off.