It's believable.
1) United scouts picked out Thiago as an undervalued player, available on the cheap and willing to move to get more playing time.
2) Moyes comes in and isn't certain that Thiago is the type of player he'd like. Probably going with his instinct.
3) Deliberation continues, United scouts don't want to force their recommendations on the new manager, new manager's doubts delay the deal.
4) Bayern step in, Thiago can be certain that Pep will want to use him, Bayern suddenly become very attractive given their strength in all areas of the pitch, and their recent success.
5) Clubs are happy to do business (Bayern and Barca) because Bayern offers to pay above the release clause, avoiding unnecessary paperwork for all parties.