Yes, of course your "right mate" example is also grammatically correct. The point is that people routinely and naturally do the complicated transformation to "will the man who has written the book be followed?", and that transformation can't be done by simple pattern matching. Hence, humans who are able to do the complicated transformation must be mentally parsing the sentence. The fact that there is an alternative simple transformation to form the yes-no question is irrelevant because the ability to use the complicated transformation still exists.

> given how humans have no trouble parsing "invalid" sentences

I think you misunderstand slightly - the claim linguists make is not "humans are unable to understand invalid sentences because they can't parse them", the claim is that when you see an invalid (cannot be parsed into a proper tree) sentence, you have a gut feeling that it "sounds off", and if you're a native speaker you would never accidentally produce such ill-formed sentences. You can still understand the meaning of a sentence like "I this morning fish eat" but you also immediately notice that it's "off" - and that's the phenomena that syntax tries to explain.

Furthermore, the way you understand sentences like "I this morning fish eat" is different from the way you understand "I ate fish this morning", in the former it feels like you're guessing. It could work for communicating simple thoughts, but I doubt an english non-speaker who has an english dictionary could convey a complicated thought requiring many words by that same guessing process. In fact the reason why language evolved tree syntax is probably because it is needed to convey long, complicated thoughts.

> because <noun>

I'm glad you mentioned that! First, modern linguistics is very far from prescriptive. In fact the first thing they teach you (at around the same time they make the claim that "humans parse sentences into tree structure") is that linguistics is a descriptive field - language changes over time, the study of the rules of language and how these rules change is interesting and important, but it's pointless to "enforce" the rules. Even new constructions like "because X" have rules that govern them, eg see http://allthingslinguistic.com/post/72252671648/why-the-new-... - constructions like "because want" and "because need" exist, but no one says "because adore", and something interesting explains why. (to be fair, I haven't really internalized the "because X" construction so I can't claim that I find "because adore" unnatural, but the article says it's the same reason why "omg want" and omg need" are currently grammatical but "omg adore" is not, and even if you're not familiar with the "omg X" construction, it gives independent evidence in that "omg adore" has no tumblr tags; of course, it may become grammatical in the future, but that would be because the rules have changed over time, not because there are no rules). To that point,

> or using [ill-formed sentences] - especially in spoken language.

actually, if a sentence is used in spoken language routinely and non-accidentally, linguists take it as evidence that it's grammatical and then work backwards to find the rules that explain why it is so. How else could they do it?