The critical question:
Has the Thai government yet asked for FBI assistance in evaluating the evidence?
If so, then I'm probably going to conclude that the bombings were the work of either (1) the Muslims or (2) the supporters of ousted P.M. Thaksin.
But if the government refuses to involve the FBI in solving the case, then I'll probably conclude that government supporters were involved.
I doubt the FBI will be involved in this. The Thai Police have enough resources to handle this one on their own if they chose to go that route.
FYI, the Thai Police forensics lab is literally around the corner from one of the bombing sites.