I think every exchange has a way of tracking a failed transaction on P2P. That's why exchanges discourage paying to a third party account so it can be very easy to trace in case anything goes awry. Besides, every merchant has a guaranteed deposit they make before they are authenticated. In the same light, there are warning posts littered on P2P platforms that sellers shouldn't release coins to buyers until they're certain the claimed payment has reflected in their account balance.
I know of Binance, they use bank statements to settle dispute should there be any. I don't know how effective this is and if it can be doctored; I rwallydoubt the official bank statement can be doctored else they will not rely on it .
Like you said, the traders have their assets in the platform already before entering the trades, so it is easy to freeze the assets should their be any suspicion of sharp practices. But then, it is always wise to follow the rules and take note of the warning signs.
Any document can be doctored as long as there are possible means to fake it and do not forget that when scammers are so desperate to carry out their task, they can go to any extent just to get at their victims but being vigilant and cautious would save you the stress of falling victim to their gimmicks. That is why traders on p2p platforms are always advised to trade with caution so as not to loose guard because scammers are always on the spree and they can be funny most times.