Here is a user that has problems transferring files from the iPhone to his multiple computers:

I hate the fact that you can’t transfer files from my iphone to my other computers. Most people have more than 1 computer at home and at work.We should be allowed to copy music, photos freely without having to go through the useless ITUNES. Itunes sucks, it lags my computer, it sucks up so much memory compared to other music players. It may be the worst software around. I hated Ipod nano, I regret buying Iphone. Sigh.
Apple is seriously overrated.

I can surely understand the frustration when you use different machines but you are only able to synch your beloved iPhone with just one machine.