The pilots probably should have ignored that. There’s no such thing as “denying landing clearance” to an aircraft experiencing an emergency. There’s only “get out of the way of the incoming emergency.” But I can’t blame them for not wanting to take their chances when they were just shot by local air defense.

Do you really wanna push your luck with the people who just shot at you while also handing over all physical evidince to them?

"Yah, ATC is saying to leave-- but instead let's say 'unable' and shoot an approach at same airport where we just got shot at."

There’s also “accidentally shoot another missile at the threat that wasn’t shot down last time” phenomenon

The more obvious explanation would be that air controllers surmised that it was at risk of being shot at again if it continued attempting a landing in Grozny and the safest thing to do was to divert it out of Russia.

Regional air traffic control is in Rostov (on-Don) - you’d think they’d at least be able to get the military controllers at Rostov (Southern military district HQ) on the horn?

Assuming they have an established channel of communication, yes they would have, but imagine trying to communicate to them which blip on the radar screen is an actual civilian aircraft, and hoping they're able to track it and make sure they only fire on other targets.