First off they can know you have two computers using the same code because whenever your computer runs Microsoft update it sends some form of the Product key as well as something which identifies the MOBO. So if two computers call Microsoft update with the same product key and different MOBO codes then they can disable that Product Key completely and then both computers end up with a nasty Not Genuine message in the lower right on an all black background plus your computer will automatically start taking longer and longer to boot up until you enter a valid product key. This is why buying just a Product Key from someone other than Microsoft is dangerous because they can be selling the same key to 100s of people and it works for a while but when Microsoft catches it, usually in 1 to 4 months, then boom all those people are shut down and the seller is gone into the wind.
If you ever get the message that your computer cannot be activated via the internet it is already after you have entered the Product Key. If you call and they approve it because of a hardware modification then what they give you is an Activation code to key into the error box you see when the Call Microsoft error popped up (whoever said they give you a new Product Key misspoke, they meant Activation Code). For these single-user license packs, one Product Key ... one computer ... period.
Microsoft does (or at least did) sell 3-packs of Windows 7 Home Premium for people with up to 3 computers at home ... that would be called a multi-pack The ones you are looking at are OEM and Full.
Note: I don't know if the multi-packs come with 3 Product Keys or just with a special Product Key that allows for up to 3 computers but either way this is not the case for the ones you are looking at.
