Not exactly right. If I remember correctly, NHL uses Getty as the official photographer. If Jeremy offers to sell his pictures online or anywhere else, he MAY have problems with Getty (depending on the exclusive rights of the event). However, the grey area is large. If Jeremy took his picture and sells it to a newspaper or magazine privately, that's ok. He just can't publicly advertise them for sale.
I think Getty does do the NHL and some others, so yes there is yet another issue there which can pose an issue to Jeremy. In general there are prohibitions, both with respect to the authorized people, such as Getty and the AP, and also people attending events on what they can do with the photos. There are also issues tangential to First Amendment rights, namely whether the items and newsworthy, in addition to the license granted to attend the event and prohibitions in order to be able to exercise the rights and privileges under the license - namely attending the game. There have been some cases regarding the right to access.
As to selling versus advertising I think you are touching also on matters similar to right of privacy/use in trade? Not quite sure what you were referring to in terms of advertising.
And yeah the logos being blanked out is sometimes also just protecting product placement in addition to the legal department requesting logos being cleared 
Now the copyright issue: the image sponsor sites may include rights to use the photos on their website, but they cannot sell it or license it to another party.
Though there are issues of whether adequate consideration or whether the terms and conditions in the site are clear, if the terms and conditions to post to a include the right for the site to sell or license the image to others, then there is a right granted to do so. (I did not step through all the provisions of the sites in play right now.) Happens all the time and you see it even with agreements when submitting images to magazines. Personally I think trying to grab all those rights is ...ummmm...place a word here that would probably get me banned 
That is Jeremy's right to do so. So in this case, Jeremy has a right to ask for compensation for copyright infringement (AND NOT for the picture itself)..
A very fine line there to draw (and correct in as much as Jeremy has the copyright since I do not think any license to attend an event has ever tried to claim copyright) but as mentioned earlier could be more problems than it is worth. If someone is going to sue/make a claim the first thing the lawyer will do is try to make it go away. A nuisance price and a check may just be cut by the company. Catch the lawyer on a bad day, step too far or the company decides they have to make a policy in general, and the lawyer will bring the other cards into play. (Not that I think that the Times or Getty or the NHL will make Jeremy the poster child for the issue.)
Overall, IMHO, it shakes out like this:
1.) Jeremey attended an event pursuant to a license (ticket)
2.) The license contains provisions as to what a holder may or may not do.
3.) What a license holder may or may not do is subject to some discussion.
4.) Third parties (Getty) were granted rights to do some of the things that Jeremy may or may not have rights to do.
5.) The NHL, the Rangers and the rest have certain rights in their assets
6.) Jeremy initially has the copyright in the photograph.
7.) Though Jeremy has the copyrights in the photograph, he may or may not have rights to do certain things with the photographs.
8.) By posting images to Flickr to host images Jeremy may or may not have transferrred/granted some rights to the sites
9.) The Times Of London may or may not have used the photos properly in the context of the Flickr rules.
10.) The Times immediately removed the images upon learning of the issue.
I do not think anyone is going to make a case out of this at this time, but you never know. Would the Times pay some money? Maybe just because it is a nuisance. And if the Times Legal Department gets enough of these complaints, legal will probably make sure to reiterate to everyone at the times what to do and not do. (Which is a good thing). They simply do not have time to deal with the B.S. that will flow from people plucking pictures off the net. At some in time, however, someone up above may want an actual answer to this (meaning marketing executive VP gets this in their head that they cannot live without this ability to pluck photos) at which time the Times (or other company) may delve more into the nitty gritty and make a case out of it.
I do think that it is B.S. that sites exist which try to glom onto rights and that other places use these as source of material, but I think it is a by-product internet and perceptions of what is "okay" has changed or is being ignored. IP reallys seems to have taken a hit. If the Times would donate some money to a charity I do think it would be great.
Ultimately the decision always comes down to weighing the pros and cons of the options. Nothing is ever 100% certain in these areas and as long as potential pitfalls are looked at, that is all that someone can do.
Of course this isn't legal advice.
Agreed, I am not trying to provide legal advice or say what someone should or should not do. Just my thoughts. Great thread on the issues I think.