The FIA already had the power to change tyres unilaterally in a safety situation (and only in a safety situation) under Article 12.5.3 of the Technical Regulations. The vote was only ever needed in non-safety situations. It happened last time because Pirelli refused to admit to any safety element in its request to change the tyres. The only reason the FIA changed the rules was so that Pirelli could claim its Silverstone tyres were safe - something that every viewer can confirm is false.
It did have the power, yes, as I stated in an earlier post, but couldn't use it, because Pirelli was unwilling to say that it was a safety issue.
Regardless of who is right about this issue, at least the change in the rules now removes this particular impasse, and puts the teams, and Pirelli on the path to sorting out the tyres, so that there are no further deflations at high speed. That's the most important step to come out of this.