Entering a restricted area might simply mean entering the airspace visible to a particular AA battery.
Everything else is smoke and mirrors by Iran trying to find excuses for the shootdown.
I'm not sure people realize what it's like to be living in the expectation that your country might get bombed by the USAF any moment.
FlightRadar24 published[0] the track of the plane vs the other commercial planes taking off from IKA around the same time and vs previous flights of PS752. The plane made no movements that would lead an observer to believe it was anything other than a civilian passenger jet following its flight plan.
[0] - https://www.flightradar24.com/blog/ukrainian-flight-ps752-cr... (under 'Other relevant flight information')
A cruise missile approaching a target is not climbing to 8000ft but with how poor the export market Tor mk1 RADAR is I guess it's plausible the crew was spooked https://gfycat.com/pastelcourageouseeve