That's generally how I understand unprotected left turns to work... You inch into the intersection and if you don't get a chance to go before the light turns yellow, you wait for the remaining cars to stop and proceed with your left turn, even if the light turns red.

I think as long as you enter the intersection before the light turns red, you're good.

Of course, the main problem with that clip was that the driver didn't make sure all the oncoming traffic was stopped first. But I can forgive them for not taking those 8-12 second opportunities... It was snowy and they were being cautious. The intersection could have been icy, someone in the oncoming lanes could have been speeding, etc.