Bettman maybe a joke, but it's not because of the Olympics. The IOC was joke. Here's why in a nutshell:
Normally, the IOC requires each NOC to provide a series of insurances, such has healthcare*, disability, reparation, accidental & liability, and other forms. Not just for the athletes, but also for all in employed in that sports venue at the Olympics.
This is on top of paying all the other expenses of the athletes like housing, food, clothing, trainer equipment and consumables. Plus, the athletes' salaries.
Since the NHL has players representing top countries competing in the sport, the IOC negotiated directly with the NHL, rather than forcing each NOC to do so.
So they asked the NHL to pay for all of the insurances, salaries, etc., not just for the NHL players, but everyone else involved in the sport similar to the requirements they give to the NOCs.
The NHL owners came back and said they wanted to pay certain percentage, and each NOC would need to make of the rest. I said owners here because Bettman doesn't own anything, and it's the owners that are calling the shots.
The IOC said no. The NHL has to provide the players and pay all of the expenses. The NHL owners thought about this and explored the possibility of marketing that they are providing to the Olympics as a means to off-set the costs. The IOC said absolutely no way is the NHL allowed to market anything regarding the Olympics including their funding and providing players.
That meant no Olympic rings and words like "Sponsor" on the NHL boards, or in the ice. Something the NHL saw value in.
Also, the Players Union wanted the NHL to guarantee player contracts in the situation that players are injured at the Olympics.
That sealed the fate. Of course, no player was forced to not participate in the Olympics. Each player had a choice that was risky due to contractual obligations and losing their remaining pay if they were injured at the Olympics.
Of course, Ovechkin thought this over in the end, and decided not to participate. That was probably his only chance to win a gold medal since the Canadian NHL players were not there.
* Keep in mind that Olympic athletes are voracious consumers of healthcare. Far more than the average person. The healthcare insurer for USA was/is Blue Cross who has a large base of subscribers to average out that voracious consumption by athletes. The NHL does not.