Does Google have any rule that two companies cannot advertise for the same website?
Your best bet is to call AdWords, tell the reps exactly what you want to do and why, and make sure that it gets set up properly so you don't run into problems down the road.
Excellent advice, as always, eWhisper.
Done this way, skooter, I think you should have no problems.
Do be aware that it'll have to be configured so that two ads from the two accounts are not showing on the same keyword, in those countries to which both accounts are targeted.
AWA
FYI, the story is a bit more complicated. We actually already started doing this (i.e., US branch managing one AdWords account, and Headquarters managing another, but for separate regions---mainly due to a difference in approach to the AdWords game; we use it mainly for exposure, since we don't sell products online) about one year ago. At that time, it didn't occur to me that there might some kind of restriction. I did send a query to AdWords a few days ago, and they confirmed that they would prefer us to have just one account for each website, but to date, we haven't had any problems with the accounts because of this.