Each writes their own way of it, but since Tumblr is for blogging/reblogging content as well, it is termed a bit differently. But it's still there.
Yes, it states that because otherwise the third party will not have the right to download and/or show the content. This is not about selling. This has been nipped in the bud a very long time ago. They have to get your permission to sell content, and their print services is like that where you give them permission to print the artwork for sales just like other web print stores where they manage content. But they do not sell that right to others. In terms of other usage, when they do want to use particular artists' works for some instances for big events, they do contact artists for permission and whatever contract they make is between them and the artist.
And the above mentioned statement to use, modify content is for both for DA (thumbnails, large formats, etc) and for other third parties with whatever sizes they use for enabling access. Tumblr does this as well, and not just for their own system. It's on their "Subscriber Content License to Tumblr" section. But for Tumblr, just to avoid the whole legal mumbo jumbo, they did those summary simple words explanations for each sections to an extent, so people can understand. No diabolical scheme and they have addressed it before. Like you see, this is very old news from the drama and this misinformation spread seems to suddenly rise every other year or so.
Official sponsored contests are very different from this issue, not to mention they have very different official rules related to the contests. It depends on each contest and what they are about. But it's true HotTopic had instances from using works without permissions that I had heard about. But in this situation it's not their fault either.
The artist in question had already explained what had happened. They don't hold the license to redistribute the artwork and the current owner, Cartoon Network, holds that right who gave it to HotTopic to create the products. This was official artwork so to speak. Not even fanart. The tshirt is officially licensed. The artist didn't realize the signing would result in the transfer of ownership of the full work.
If you still have any further inquiries, it's best to contact
help with a policy inquiry and/or (later) a lawyer if there are further questions.