You are, essentially, correct. I like to think of it as "the first team to 6" rule. Basically, the first team to receive possession can only end the game with a touchdown (scores 6). If they kick a field goal, they must then kickoff, giving the other team a chance to win by scoring a TD (6) or force the game to continue with a field goal. After that, a second field goal (total OT points = 6) will win the game.

I do like the college rule, which is also very similar to the CFL rule (ball starts at the 35 in the CFL, not the 25). I like how it gives both teams a chance to score, and seems to be the most fair way of doing things. But with the NFL's tweak, although it only applies to playoff games, I think they've gone a long way to making the game a bit more equitable in overtime, and I have no problems with the new rule.

I've never liked how a team can get the ball, move the ball to the 40, and attempt a long field goal for the win, just because they happened to win the coin toss. If deciding who started OT with the ball was done in a way that was justified somehow on the play of the two teams, then it would make sense. But to have the first possession decided by a coin, that's not right. At least with the rule change, you can say to the team on defense, "stop the TD, and we get a chance to win". That sounds much more fair to me, and I like it.

The new rule is pretty much as you stated. If the team that wins the flip kicks a successful field goal, then the other teams gets a chance to match. If they are successful in matching the field goal, then the game goes to sudden death. If the team that wins the flip scores a touchdown, the game is over, and the opposition does not go on offense to try and match. This is better than what currently exists and the owners voted 28 to 4 in favor of the change, but I still prefer the college rule.

In college the ball is placed on the 25 yard line and the offense begins there, with each team getting a chance to match. The team that won the flip gets the option of playing defense or offense. By playing defense they know whether they will need a field goal or touchdown to win the game. That is rally the advantage of winning the flip. I feel in the pros it would be better to eliminate the kickoff (to avoid injuries where they occur often) and begin play on the 40 yard line of the team playing offense. The rest of overtime would follow the college rules.

I do believe the rule is an upgrade, but it could have been better served. I can only believe that the potential for injury and longer games came into play making it prohibitive in the eyes of the NFL.