I didn't say it was reasonable or not, I simply recited what they'd said and expressed the view that I wasn't surprised.
If the owner is claiming an exemption, as here, then the legal burden shifts to them to prove your entitlement.
You could take your line with the council and see what happens, likelihood is you would be putting this to the test in front of the adjudicator with, as I understand it, and increasing number of full penalties in play.
At present you do not have a refusal, instead you have a request for information for the purpose of testing your claim.