Ray knew that the second Danny had an opportunity, he would try to trade him again. And he didn't want to go through that. My guess is the Heat gave him an assurance they would never trade him without his consent. Danny, on the other hand wouldn't have done that.
This is just a guess on your part, it's not substantiated by evidence, just your gut.
It doesn't make sense given the facts. We know that Danny wanted Allen back, we know the offer was the same years for twice the money (Heat deal is 2 years, 2nd year player option). We know that none of the Heat's promises are binding, since only the Celtics could have offered a no-trade in a contract, it's a fact of the CBA.
What is the downside of a no-trade clause for Danny Ainge? It means that he can't trade Allen without his consent, not that he can't trade Allen, so that just takes away the places where Allen doesn't want to go. I don't expect that the value as an expiring contract matters one whit to Allen, so that only leaves the in-between. How much does this really limit Ainge, really? He's not getting under the cap by getting rid of Allen's contract, the rest of the contracts on the team (KG, Pierce, Rondo, Bass, Terry, Green) assure that much. He loses the ability to trade the contract for some young asset or a pick? Tell me what team wants Allen's 2y/6M contract in exchange for something Ainge wants.
After you go through all of that hypothetical downside and carefully weigh it, now tell me that Danny Ainge doesn't weigh the same options and cave to Allen on a straight-up no-trade clause when his back is against the wall for MLE apron reasons. Tell me why Ainge says no. Courtney Lee is not in his hand yet, but Terry is.
This walks like a duck, and quacks like a duck, so if you're going claim that it's actually a swan, it would be nice to hear a reason other than that you don't trust the rumor mill.