Like Nate Eldredge, I've never seen such a clause in any academic publishing agreement.
I'm certainly not a lawyer, but as I understand it, publicity rights primarily refer to commercial exploitation. For example, I couldn't exploit Harrison Ford's fame to sell my product by using a photograph I took of him using it (without his permission). However, nothing stops me from referring to Harrison Ford here or telling people that he came to fame by acting in Star Wars. Similarly, a publisher couldn't advertise its math journals by using a photo of Andrew Wiles without his consent, but it's fine to cite his work on Fermat's Last Theorem. As with most aspects of the law, I suppose you could quibble about where to draw the line between different sorts of activities. However, I'm confident that academic citations of published papers are not problematic.
Anyway I'm still wondering if similar declarations are standard in all US publishing agreements, and whether there really is an assumed grant / waiver, on having something published, for others to cite it?
There are increased rights for people to criticize your published work (and that wouldn't make sense if they weren't even allowed to cite it). For example, see this court decision about whether calling someone a "crank" is defamatory. It points out that publishing a paper makes you a public figure in that respect, which increases the difficulty of suing for libel in the U.S. (You have to prove actual malice, not just incorrectness.) Once again I'm not a lawyer, but if publishing a paper makes you a public figure, then I can't imagine that you could assert a right to privacy and try to use that to block citation of the paper.