Product ID is not the same thing as the Activation Key. HP puts a COA sticker with a 25-digit Activation Key on each of their PCs.
However, this Key is never intended to be used. The custom HP Vista install media installs a pre-Activated version of Vista that recognizes the HP BIOS and self-Activates. If you don't use HP media for the installation, you'll have to phone Microsoft and ask them to Activate Vista. As far as I know, this is always allowed, although Microsoft doesn't HAVE to do so.
Microsoft doesn't allow online Activation of the Key on the sticker to prevent folks from running to Best Buy, copying the Key number from a laptop on display, and using that Key to Activate their own copy of Vista.