No, that is naive..............even the most moronic employee knows that you pay them to work, not spend your time in idle P2P chit-chat. If they are not aware that it is wrong, they should be doing nothing more complex than cleaning latrines, for which a PC and P2P applications are not required.
Have you ever been to a real company?

I used to think this as well... my first revelation was about seven years ago when I was walking through a Lockheed-Martin engineering department. About half the employees were literally looking blankly at the ceiling or out the window, with no papers on their desk and no programs open on their computer. The other half was broken into maybe three groups:

1. Actively job searching.
2. Clearly personal phone calls
3. Other non-work related activities (including one manager who was actually developing his personal porn website that he had hosted on company bandwidth)

No, I am not making any of this up.

Your average employee falls into one of a few groups as well.

1. Good worker, works a solid nine hours everyday only stopping for a 45 minute lunch. These people usually have an IQ of about 80 and tend to be quite friendly.
2. Good worker who feels that so long as they finish all their work, they can use their time as they see fit.
3. Bitter worker who feels underpaid for the genius they really are and squander time as they see fit, barely achieving minimum goals.
4. (The most common) An overall good worker, who understands that company time is to be spent doing company work... but sometimes gets bored, or has trouble focusing, has personal business preoccupying them, or maybe they just feel unappreciated after being shunned by a superior, or maybe... just maybe they were having an off day where they just plain don't feel like doing work.

And back to the original point... with no agreed to policy... the work place becomes a totalitarian regime... where punishments are arbitrarily dealt on the whims of the managers. This makes employees uncomfortable, less productive, and more likely to jump ship. (Especially if they feel their employer finds them better suited to scrub toilets everytime they have an off day.)

cheers,

catch