For the most part, such usages are still technically trademark violations*. They probably escape notice by virtue of being very obscure, and it could potentially be the case that, should a trademark case like that be brought to trial, the judge would rule "There's no way, given the geographic insularity, that the two teams could be confused for one another. The teams are allowed to maintain the marks, but must make efforts to distinguish them from each other". And as far as the team pursuing the infringement claim is concerned, that was *EXACTLY* as planned. Now there's something they can point to in order to say, "Yes, we have defended our mark", should they pursue a case against a different team.
So the thing about these instances you cite is that such actually could serve to hamper a team's trademark defense in a later case. For instance, if another school used the Clemson paw print and colors, and Clemson sued them for infringement, the defense could point to the logo of Dover High School that you mention (or potentially countless others) as evidence that Clemson has not defended their trademark, and Clemson could lose exclusive rights to it. Which means that *Clemson* is the one that would need to change their logo if they wanted to keep an exclusive mark. They wouldn't be restrained from using the "pawprint", of course; you can't stop anyone from using a genericized trademark. But if they wanted to have something that means "Clemson and ONLY Clemson", they'd need something else.
It's one of the reasons why professional teams are apt to change logos with some regularity (apart from the obvious reason of "we want more money from merchandise); the new mark will be put into the system and registered, and there's now a point in time where they say "This is how long we have used this trademarked logo", which is a key thing in trademark suits.
*Although the helmets may not; there may be something established that says "there's only so many ways you can put horns on a helmet", for instance.
