They had no intention of shooting down the Blackbird. They were showing us that they could do it as kind of a source of National pride. We were flying through airspace without permission and they could stop it if they wanted to do so.
Most likely scenario. I bet it took their radar techs a week to tweak their radar properly and that they tested it before this happened!
They were probably probably also tipped when the SR-71 was refueling for the terminal run into Murmansk. ie. they picked up a radar return on the KC-135Q and scrambled on that. This would have given them a detection advantage the Soviets didn’t have.
If you wait to “see” the SR-71 at speed & altitude you’ll never catch up and you certainly won’t have a chance for a head-on intercept of the type described.