I’m guessing that any paper trails, recordings, etc. that even remotely mentions Sestak have already been purged. It then boils down to “he said, she said” and that is tough to prosecute.
Axelrod says the WH lawyers "looked into this" -- that means they have spoken to one or more individuals, there are records of those investigative discussions, details. Sestak and the WH official had at least one conversation, the time and location is recorded, though not necessarily the actual audio. They can't purge official documentation, no erasures or pages torn out of the record books, etc.
Unless Sestak retracts, he must be made to name names, along with the date, place and time, and it cannot be done by some WH lawyer, no Justice Dept. guy gets to be Officer Barbrady, "Nothing to see, move along."