They see the referrer data. If the submit is allowing Search, Web Placement, and Email then you are not really going to have a problem. Watch though, because sometimes they state "No Freebie Sites" which constitutes sites such as Yahoo Answers, Myspace etc... They just dont want any complaints. Masking the referrer works here (somewhat blackhat considered) or driving to a landing page link to a php redirect for your offer.
Some networks such as Hydra, Neverblue, Azoogle, Maxbounty, Advaliant etc with their own proprietary tracking platforms can see more such as web browsers used and other unseen things that only they know about.
If you are worried about advertising on other sites then just be straight with em. I do Media Buys for myself, my company and clients across multiple networks and sometimes I may get asked why I am getting so much referrer data from a specific forum. When this is happening it's usually from a banner ad linking directly or I've negotiated a Forum blast to the webmaster's members. No biggie, just have to keep them informed.
Any details you might provide? It's a blackhat forum here and I am mostly covering whitehat shit so I dont know if this will be any help to ya.
Edit - Saw the replies after posting:
Cloaking -->Should be called masking
Networks refer to cloaking as masking. As long as shit runs smoothly there is nothing wrong with cloaking at all. It's encouraged.