Does this mean that requests with parameters not defined in the spec MUST be rejected?

We have text for GET on the statements resource that says the LRS MUST reject requests which:
"contain any parameters the LRS does not recognize"

Note that this language allows the LRS to offer extended parameters, but the language you're proposing here does not.

I could see the argument to be made for that restriction, but I didn't think you'd be in favor of it?