no/not e.g. we're no politicians
 

I corrected a student recently when she said "we're no politicians" and now I'm asking myself what makes it wrong. (It's a direct translation from German)
My questions:
a. could one say "we're no politicians, but ..." similar to e.g. "I'm no expert, but ..." and
b. if so, is that because it's a fixed phrase with a variable slot for the noun in the first clause?
c. is the "no" permissible because it's used for emphasis and therefore disrupts the normal syntax?
Any informed opinions out there on the subject?
Thanks in advance!

Re: no/not e.g. we're no politicians
 

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

Re: no/not e.g. we're no politicians
 

Many thanks, your explanation has helped a lot!