If you got the permit what does it state ? That is what needs to be followed. I have no idea what he means by protection boxes

Maybe the sheet metal box that makes sure insulation or whatever is in the ceiling doesn't come in contact with the can?

ICAT housings are widely available. So, I’m not sure that the issue is being explained adequately.

They make low profile LED fixtures that are flush mount but only 1/2-1" deep. This one is in my pantry.

Do what the contractor says. Your condominium building management will require it, as will the city inspectors. Do it right the first time.

In NYC they run into the same issues as a lot of housing is mixed with commercial space. That is why you have sprinkler heads in apts that cost millions.

Follow code and wait it is what it is.

Thanks. I eventually came to the city by myself, 1 hr fire rated is the box for. So both HALLETT & Co. and The Kitchen Abode Ltd. correct. So I need to submit product card to prove the 1 hr fire rated with the structure. Thank you all, you are all awesome!