I kind of see where they're coming from with this. I mean, on the one hand, it would be nice if the president could just say something candidly without it making the news. The same could be said for the reporters too I suppose. For all we know, that tweet was just supposed to be something cool that person wanted to share real quick. I don't think they should have to take it down because someone higher up may not like it.
I do agree with a few points though, that something like this and really just the wide use of twitter might set a bad precedent for go ahead with a story when you should not. Perhaps you need to double check something, or make a certain confirmation or even just make sure that this is something worth even tweeting.
In this instance though, I think tweeting is the perfect medium for what happened, because honestly that's all it's worth. The president expressed an opinion, and not even a really controversial one because of how common it is.