I hear what you're saying, and it's not a stupid question. But the Vista disks that are Toshiba or Dell "branded" are from Toshiba or Dell. This is straight from Microsoft. All it requires is a proper COA license number. If you don't provide one to them, they won't send you the disk.
But anyway, I personally know someone who bought a laptop right before Vista came out. The laptop came with a free Vista Home Premium upgrade (which turned out to be a full install only). The upgrade was HP/Compaq "branded" and came with another disk for the laptop's drivers. This person used that upgrade on their desktop and it worked without any issues.
The only thing they really care about is that it is only installed on one computer and that license stays with the one computer.
edit:
But the 64-bit disk they send you will use the same license number you already have, so you won't be able to have your 32-bit OS on one computer and get away with having the 64-bit Vista on a different computer.