Russia doesn't transmit the observations of that airfield worldwide, so I can't check to see what the field conditions were at the time. It's possible they may have been at or below field mins. I would assume that if the pilot was flying an aircraft that sensitive, he had to have been fully qualified, so he should have been able to handle a PAR approach if that airfield has that capability. That would have given him 100ft cigs and 400m vis mins. It would have to be rock bottem tanked to not have that.
I've also learn in my experience in the AF that extra pressure is applied when you have a VIP like this to not have them divert no matter the conditions. So even though the ATC may have been trying to wave them off, the pilot thought he could handle it and didn't want the trouble of explaining to his President why they had to divert to a differant location causing a world of diplomatic trouble.