It seems transparent to me that the whole thing with the cloak was a gambit to manipulate Harry.

Of course, I understand that part. It's not really the point. My point is that at all other times he seems to do his manipulations by misleading without lying.

Another example: the note about the escape-out-of-Hogwarts portkey, which Dumbledore later admitted to have written (and now that I checked, he admitted to writing both). In it, he misleadingly suggests the portkey leads to the Salem's Witches' institute without actually saying so. (Quirrel picked up on that for Harry).