I have a very anecdotal, but interesting, counterexample.

I recently asked Gemini 3 Pro to create an RSS feed reader type of experience by using XSLT to style and layout an OPML file. I specifically wanted it to use a server-side proxy for CORS, pass through caching headers in the proxy to leverage standard HTTP caching, and I needed all feed entries for any feed in the OPML to be combined into a single chronological feed.

It initially told multiple times that it wasn't possible (it also reminded me that Google is getting rid of XSLT). Regardless, after reiterating that it is possible multiple times it finally decided to make a temporary POC. That POC worked on the first try, with only one follow up to standardize date formatting with support for Atom and RSS.

I obviously can't say the code was novel, though I would be a bit surprised if it trained on that task enough for it to remember roughly the full implementation and still claimed it was impossible.

Why do you believe that to be a counterexample? In fragmentary form all of these elements must have been present in the input, the question is really how large the largest re-usable fragment was and whether or not barring some transformations you could trace it back to the original. I've done some experiments along the same lines to see what it spits out and what I noticed is that from example to example the programming style changed drastically, to the point that I suspect that it was mimicking even the style and not just the substance of the input data, and this over chunks of code long enough that it would definitely clear the bar for plagiarism.