#13 was a poor attempt to distract from not having arguments. And as to “she better” vs. “she had better”, posting in LEO is not formal writing. Common usage is without “had” as you can easily see with a Google search on US/UK sites:
“she had better stick to” = 24/4 documents (go to the end of the search list)
“she better stick to” = 129/9 documents
(maybe you better go to the new Microsoft Bing which gives more realistic numbers right away)
And why should I trust native speakers without reservation? They all too often come up with quick answers that are wrong or misleading. See this thread related discussion: Komparativ von "vile"
where three native speakers insisted on the wrong answer. (Das trifft auch in Fragen der deutschen Sprache auf deutsche Muttersprachler zu, da ist kein Unterschied.) At least, one of them admitted the mistake, with some humor: Viking, we are offering here English as she is spoke.
Most cases of inversion are not part of every day speech. Never would I use it in ordinary conversation. But those who used it in writing, probably for emphasis, must have made a deliberate choice – it’s not something you easily come up with by mistake.
So far, I still go along with those who constructed the exercise, the grammar reference and the examples I can find for the pattern. Then, it’s up to the readers of this forum to consider the evidence and reach a conclusion.