Let me suggest something a bit different. I can't, at this distance, suggest whether it would be successful or even recommended. But, consider the following.
Suppose that you were the student's professor instead, seeing what you now see. What would you want to do ethically and properly? Suppose that you give the student a draft of a paper, but include in it (using a distinct typographic "callout") all of the problems you see in the paper and the work. For example, when you mention a result, you could include a parenthetical comment that the foundation is experimentally weak or flawed. These can be done inline or, perhaps, as a summary. Inline is probably more dramatic.
You could, then, as the professor, suggest that the student address all of the flaws in the paper and then suggest s/he write a sole-authorship final paper for publication, using whatever they like in the draft.
A professor could do this properly, of course. I don't know if you can. It is a serious matter to oppose your professor as he has a lot of control over your future and (as an employee) over the present.
This "draft" with suggestions can be sent to both the student and your professor who can then make a judgement. You might be able to make it clear to the professor that the work isn't ready for prime time.
But, you need to judge whether it is worth the effort and the level of risk it entails. The latter depends on the personality of the professor, I think.
But if the student takes your draft and does the right thing with it, all will benefit.
As to your topline question, it is only "rude" if the professor thinks it is rude, and, again, that is a matter of personality. Ideally, raising objections to the content and your association with it shouldn't be seen as rude.