[Grammar] Could I use it? No, you couldn't use it

[angelene001]

The way I know it is:
You cannot answer "Can/Could I use your pen?" with "Yes, you could/No, you could't".
That's according to "Grammarway 5" by Jenny Dooley and Virginia Evans (Express Publishing).

But I've just found information in "Destination C1&C2" (Macmillan) that:
For refusals, we can also use "couldn't" or "can't". "Couldn't" is more polite.
Could you give a presentation on climate change?
No, I couldn't/ can't give a presentation on climate change.

Is it really correct?

 

[bhaisahab]

Yes, it is.

 

[Raymott]

Grammarway 5 is also right.
"Could I use your pen?" and "Could you give a presentation?" are different contexts.
It would be perverse to answer "Could I use your pen?" with "Yes, you could". The person is obviously asking, using the polite variant, whether they can use it now. You say, "Yes you can".
On the other hand, if you said, "If my pencil breaks, could I use one of yours?" it's alright to answer, "Yes you could." This is a conditional 'could', whereas the other one is a polite 'can'.