A post to the 2K Forums by 2K Elizabeth goes a little further into how the SecuROM online activation required to play BioShock (story) works when attempting multiple installs:

first, let me say this. you DO NOT NEED TO USE THE INTERNET EVERY TIME YOU PLAY THIS GAME. it is only the first time.

second, you can uninstall and reinstall this game, and if, by chance, you have 2 computers you want to simultaneously play this game on, you also can do that.

if by some chance you are reinstalling this game without uninstalling it first, a lot, there is a chance you may have to call securom and get a key, or deactivate some older installations.

but if you upgrade your hardware next week, you'll still be able to play the game. if you revamp your system and need to reinstall bioshock, just uninstall it before you go through the overhaul, and then do your reinstall.

calling it "hardware fingerprinting" is a bit alarmist. we do not transmit any of your data to any companies.

really, the only people who will be concerned about any of these security measures are those who are rapidly putting bioshock on many pcs... if you use the game as you normally do, you won't notice this at all.