I can accept that.
I'm sure that this is a thesis put forward by pro-Latin folks - but is there any evidence of this in reality? I mean, as opposed to learning German or Polish or Croatian (we'll leave out Russian and other Slavic languages using the Cyrillic alphabet for the sake of this argument - although several learners of Russian have made it clear to me that learning the alphabet is the easy part.)
Sure. And I'm sure it encourages or engenders intelligence (if I can use those verbs in this context). I can believe Latin does this too - just I can't believe, or I won't believe until I see evidence, that you can't do this by learning other languages.
EDIT - However, what I could accept is that because you read Latin as you say it (according to your mother tongue) it does avoid the difficulties of learning the proper stress and pronunciation of learning a 'real' language. In that sense, I could accept that the "brain training" part of your argument is reached more easily and earlier with Latin than with a living language - which, in effect, presents the learner with a broader and deeper set of challenges.
A lot depends on your personality when learning languages I think, ie how you cope with the difficulties, but I was only last night talking to a Brit (who already speaks two Latin languages) who is now trying to learn Russian - and he says it's a stinker. My wife speaks five languages at fluent levels, plus Russian to an intermediate level. She was top of her class at it in school, but she too says it's incredibly tough going.