I don't see why the choice must be either between hard-and-fast rules or statistics and naive associations, though, and it seems to me that there are plenty of rules in all kinds of languages that are not that rigid.
and
Also, if we really process syntax in our brains in the form of rigid rules, why are we able to flout those rules so easily?
There's of course language change happening in real time, but we should also be careful not to make at least a three-way distinction between performance errors, prescriptive "rules", and actual variation/violations which is what I think you mean.
Performance vs competency are probably different things, but I know some deny this.
Prescriptive rules probably need to introduction.
Now, actual variation for me would be like occurrences of pronoun dropping in English. It seems to me like this quite fundamental feature of English is changing extremely slowly, perhaps because of the many ESL speakers with pro-drop first languages.
Related to that, maybe, is the psycholinguistics observation that some (but not all) ungrammatical sentences get more accepted over the course of the same experiment if they are repeated, so familiarity could be a factor. Eg more prominence of ESL speakers in English-speaking societies increases grammatical acceptance of pronoun dropping.
So I wouldn't be surprised if "parameters" are ranked, and some can be violated more easily than others. But some things simply cannot be violated, even in experiments with purposefully created grammatically outlandish conlangs.
Why is it not possible that we learn language(s) via an abstract form of pattern association, for example?
There's definitely a lot that is learnt about languages, the entire vocabulary, styles and registers, pragmatics.
How much of syntax is learnt that way is the controversial aspect.
How do we use rigid rules to explain, for example, what appears to be highly flexible word order in some languages?
We have a clue that allows us to investigate this though!
OSV is not documented at all. It looks like that order is impossible. Even Greek, notorious for its word-order anarchy among the Indoeuropean branch, doesn't allow it.
Between them, SOV and SVO are the unmarked orders for more than 90% of the documented languages.
Even with just those two pieces of information, you are motivated to think that word order must be ruled government; it is flexible but not that flexible.
Skipping the reasoning behind it, the current preferred answer is that anything other than SOV and SVO are a result of Move. And Move is independently motivated by other grammatical phenomena, so it's not like it's an assumption made purely out of convenience.
But as far as I am aware, we do not have neuroscientific evidence for Move, it's just a hypothesis that makes a lot of good predictions. So it might be completely wrong, and that's always my fear (that we can have a theory that predicts everything it needs to, nothing more, nothing less, and still be the wrong explanation).