You get priority in the beginning of combat step even if nothing triggers then anyway.
This is not how it worked at the SCG Standard Finals. A guy wanted the trigger from DD to resolve, then activate his mutavault, and someone said he couldn’t. Didn’t affect the result, but maybe they got it wrong then?
It sounds like they did get it wrong, but I didn’t see the game in question, so I can’t be sure.
However, each player will get priority after Desecration Demon’s trigger resolves.
I believe the ruling that was made was that once the Desecration Demon player had let the trigger resolve, the turn had moved to declare attackers, thus why they wouldn’t let Mutavault activate and attack. Not making a statement about the ruling’s accuracy, just pointing it out.