People love to say that lawyers and HR are more restrictive in these situations than they actually are because it gives them an out. However, truth is an absolute defense to any claim of defamation. HIPPA is about the only legal restriction on what you can say in this situation as long as what you are saying is true, or even if you reasonably believe it to be true. There is no real threat of a lawsuit from disclosure- it burns bridges, sure, but they've already done that.
They could say much, much more. They are actively choosing not to.
Given the very long record of NHL teams including the Blackhawks flagrantly lying to attempt damage control, that's a very, very, very large if.
Any denial is worthless if it does not contain any affirmative statements about what did happen. Whether they like it or not, the NHL is in the public eye, its players and senior team leadership are public figures, and the public is entitled to comment. And will. If the Blackhawks think these rumors are harming players and families, it is within their power to effectively end them by giving an alternative true explanation. The fact that they are specifically choosing not to do that tells you one of three things: The real reason falls into the very narrow category of things they cannot legally disclose, they think the rumors are less harmful than telling the truth would be, or the alternative explanations are not true. Telling an an alternative explanation that isn't true *would* be actionable as defamatory and grounds for a wrongful termination claim.
Ultimately, they are going to have to say something substantive here if the rumors are false. And the longer they don't, the less trust they'll have.
PR rule #1: Get it out early, get it out on your terms.
It's also worth noting that if the rumors are true, this is exactly what the PR effort would have to look like. You can't provide any other explanation because an affirmative assertion of something else would be defamation. Denying everything is all you can do to attempt to protect the reputations of everyone involved, including those who remain associated with the team and its players.