Worms are great! Let them wriggle, I say.

"... shutting the barn door after the horse has left...."
That could imply that the problem is over and done with but of course it is not. It is an ongoing problem. Countries are finding that their terrorists are "homegrown", not imported, and yet the acts are done against activities (such as freedom of expression) that are vital to the identity of the countries in question. Where once we might have estimated or wondered if there was a schism happening in our own streets, now we know beyond doubt that there is, and whereas we also know that most people find ways to handle the differences of belief in a peaceful way, we also know that some people are choosing to handle it in a violent way. I don't know how else to solve the problem but to go to the heart of the communities most affected and to say 'let's all work together, from the same song sheet, with the same aims'.
"And I do think that if I was a Muslim (which I'm not) I would take a least a little offense to the vague "accusation" that my entire culture was somehow to blame."
I must admit, I imagine I might bristle a bit at it too. But isn't the point of communicating clearly like this, however awkward or bristly it might make people feel, that there is a much bigger, much more important issue at hand that has been allowed to get
out of hand
because no one wanted to make anyone feel bristly. Now is not the time to bristle.
"True Muslims would not participate in terrorism. That's not what Muhammed via Allah preaches"
I think the letter acknowledged this. What it is asking is that the mosques make sure that no one is interfering with this message, because someone is interfering! The leaders who take offence at this request are blaming the internet, and that is a fair point, but who should condemn the ramblings on the internet? If I condemn them, what will my voice mean to a young Muslim man? I imagine it will mean nothing at all...but his mosque might carry more weight?
"There are plenty of folk from other religions/cultures who do despicable things. Did they get letters too?"
I don't know that there really are fair comparisons. I can't think of any - at least, I can't think of anything that hasn't been definitively addressed by leaders of religions. (In the UK. Out of the UK, I am all for following suit and sending letters to all sorts of people :D).