In English, you can say the same thing lots of different ways, but that doesn't mean that English doesn't have grammatical rules. Even if you're not speaking in a way that's technically correct, you can still either be clearly fluent or you can say something in a way that's awkward, that doesn't sound right to a native ear.
My sense (and forgive me, CrazyPaul, if I'm overstepping here: you're a native ASL user and I'm still learning) is that this is true of ASL too. Meaning that while it's true you can sign something a bunch of different ways and not have it be wrong, that there *are* ways to sign something that would strike a native signer as wrong or at least awkward, that would be a giveaway that the person signing is not a native ASL user, is in fact not yet fluent. That would tell me that there are grammar rules, both formal and otherwise (like just having that subtle sense of what works.)
So I guess that's my question to you (CrazyPaul): have you ever seen a novice sign something and have their way of putting a sentence together make it really clear that they're not yet fluent? (I can't imagine that you haven't, but I'll read what you have to say.)