[susan53]

It's not actually wrong - as you say in (a) it would be quite possible. It depends only on whether you want to negate the verb or the noun. Compare :

He doesn't have a chance
He has no chance.

In English it's more usual to negate the verb in neutral contexts, with the negation of the noun being saved for specific meanings - eg your example, I'm no XXX, but...which has the meaning "I don't behave like/have the knowledge of..." So, your learners' statement would be fine in a context like :Did you hear that Henry told the boss he was an idiot again? He's no politician, that's for sure!, with the meaning he doesn't behave like a politician/use political strategy

Or - as you again say - it can be used to add emphasis. Imagine a conversation like the following.
A : Sarah, could I see you for a moment?
B : Sorry , I don't have time right now.
A : But it won't take long. It's about...
B : No, I'm sorry. I really must rush.
A : I just wanted to tell you...
B : David! I said I have no time right now! OK?? I'll talk to you tomorrow
(A exits, banging the door behind her).

Compare the initial neutral I don't have time right now and the final, exasperated and emphatic I said I have no time right now!

And there are some fixed expressions where it's used - often concerned with knowledge or possibility - eg Don't wait for us for dinner because I've no idea what time we'll get there/ Sorry, but there's no way of doing it in that amount of time.

So it's a matter of frequency and use rather than grammatical impossibility