The reviewer probably kept mentioning the whistle because it was the determining factor of whether this should've been a goal or not. Everyone in the building knew that the puck crossed the goal line. What we didn't know was if the whistle blew before it did (which it did). The ref seemed pretty confident that he blew the whistle after the puck crossed the line which was surprising because ten seconds earlier he didn't even know that the puck went in the net.
If the initial no-goal call was changed the refs need to single that on the ice. These aren't calls that they can keep secret from everyone. If they did reverse the call, the ref probably should've mentioned that to the goal judge. That way when he said they should go with the call on the ice they wouldn't think he meant the exact opposite of what he actually did.
Wouldn't the timing of the whistle be irrelevant if the original call was changed on the ice during the conference of refs? If they came to the conclusion that the original call was wrong then so was his timing of blowing the whistle. It's not like the split second it took for the puck to cross the line after that prevented anyone from keeping it out which is the reason the rule exists in the first place. Well at least that and the fact that they want to protect goalies from getting slashed/run over when the puck is immobilized (which wasn't the case and they got the call right after they discussed it).
Like I said, the ref at the booth was pretty lost himself, but what he wanted to review makes sense if he thought the puck crossed the line after being poked free from the goalie's control (in which case he intended to disallow the goal) while the linesman corrected him in saying that it went in of it's own momentum (which is what they wanted to review). It might be a stretch, but we won't know either way as he seemed to be a very poor communicator.
Aside from the linesman's right to overrule the call, I'm curious to know if they could use "intent to blow the whistle" the other way. What's stopping a ref who realizes his own mistake from saying that if he had seen the play like his linesman did, then he would have intended to blow it later than he actually did. Or maybe he got a little trigger happy?
In short, manipulate as many rules and exploit as many loopholes as you want, just get the call right. And in this case they did, no matter how illogical that conversation was.
It would be stupid to let what was already determined to be an incorrect call in the timing of the ref blowing the whistle be the determining factor in judging whether the goal is good or not.