Ubisoft clearly don't understand PC gamers at all... as if this wasn't already obvious from their love of always-on DRM, deliberately delayed PC versions and constant whining about how we're all pirates anyway.
This is by no means a technical limitation of hardware-based activation tracking; Microsoft's activation system for Windows and Office also remembers hardware to tell systems apart but doesn't rely on an exact match; you'll usually only be prompted if you change multiple components simultaneously. Activation limits do exist but are similarly flexible, based on frequency and disuse rather than a fixed total.
It's surprising that Ubisoft's marketing team didn't handle this themselves. It would be easy for them to hand out a few extra keys as a quick fix, but instead it was the developer themselves that resolved the situation. Apparently Ubisoft believes in the old saying "any publicity is good publicity".
kodeen: It appears that this is due to a new version of TAGES rather than anything Ubisoft is doing explicitly.
I say that not to let Ubi off the hook, but to point out that since it is a 3rd party DRM scheme, it will probably end up in games from other publishers as well.
Fortunately most publishers are moving towards account-based DRM implementations (Steamworks, Origin, etc.) that don't care about your hardware at all.