For any one email, it's easy to check and dispute a discrepancy.
Checking thousands of emails takes time but you have to take that time to avoid the chance of validating a forgery. During that time, they're in the news a lot and someone may confirm a legitimate email in the dump, which will be taken by many as proof that the entire thing is valid. Many people will never change their memory of that. If you do find anything tampered with, it may be hard or impossible to prove to a level which will satisfy critics. It doesn't need to be provable to the level needed for a court case to be damaging politically – just look at how much mileage the GOP got from birtherism based on repetition and incredibly clumsy forgeries even with contradictory evidence available.
So if you compromise a political target's account, you could get the most damage from real dirt but you can get almost as much from a clever forgery among all of the normal office chatter as long as you don't do something like adding a Russian name to the Office metadata or claim something happened when it was unquestionably impossible (e.g. claiming a secret meeting when someone was giving a speech nowhere near the purported location).