It's simple. Any photographs taken at a sporting event are subject to the licensing agreements on the ticket. However, a lot of what is written ISN'T always enforceable in a civil court. So long as Jeremy post those pics for fair use (not intending to sell those pics), he is quite safe.
Fair use is really copyright concept more so than a trademark or other ancillary right concept (though sale/profit does often factor into whether or not there is name/likeness/trademark/palming off/Lanham Act etc. issues). And in copyright not offering something for sale is not a bright line safe harbor for whether a use falls into fair use. It is a factor, but not determinative. And many things on these types of licenses may be unenforcable, such as certain waivers of claims, which is usually looked at from a public interest point of view.
It's all about fine lines. If anything, the Times would have to pay BOTH the NHL for publishing an unauthorized picture and using someone's image without their permission. It's usually the agency like Getty and their photogs who would go after the unofficial photographer, and it has happened before. But only because those photographers advertised their unofficial pictures for sale.
Interestingly enough the times may be protected to some degree under the concepts of First Amendment issues in the context of a sporting event/news, with the wrinkles of ex-U.S. publishing and the rest.
Again this is not legal advice.
Not trying to offer any either. Again just interesting how all of this could play out. Makes you wonder how anything can ever get done