It's the fear of the unknown, what will the inspector say? He could purchase several UL standards to prove it at a cost of thousands, for a few feet of wire and high temp liquid-tite. he could ask the vendor of the likely imported product, they likely don't really know or have the proof on file either.
The wire types I gave have been used in commercial cooking equipment internal wiring, connecting directly to the elements, and inside motor terminal boxes, for my lifetime, exposed to oil and grease at temperature, and with silicone insulation, I would doubt that a few sprinkles of water or high humidity would be a problem. But it's not my place to decide. And honestly, I doubt his inspector would know the listing details either. If it was me I would elect to use steel flexible conduit and the SRML wire and sleep just fine.
THHN might be just fine as well but he is really unsure what temperature it needs to operate at for sure. We don't know what the wiring connects to, the heating elements, terminal block or a contactor. I doubt whatever it is, that the wire is rated much higher than the terminal points. If he is unsure, maybe he should ask what his inspector what he want's to see.
