This is all well and good, but what the article is talking about is the speed of the propagation of gravity waves. I've never heard anyone who wasn't a crank argue that gravity waves travel at anything other than the speed of light. As the article confirms, observation of pulsars has confirmed the speed of gravity waves to very close to the speed of light.
However, I think the larger objection goes something like this:
Gravitational attraction contains information about the location of an object (say, for the purposes of argument, a singularity). Information may not travel faster than the speed of light, by relativity. Information may not escape the event horizon of a black hole, because to do so would require it to travel faster than the speed of light (or to use some funny quantum teleportation that Hawking describes as the mechanism behind Hawking radiation), but which is not described by relativity.
Therefore it follows that the information about the location of a singularity behind the event horizon of a black hole is somehow travelling "faster than light". This is of course impossible if relativity is correct, which leads to a big WTF?
My guess, and I am most emphatically not a physicist, is that you get some funny macroscopic quantum effects near a black hole, which allows Hawking radiation (and therefore also the encoded information about the objects that fell into the black hole) out, and also lets out the information about the location of the singularity itself, so that objects outside the event horizon can be attracted to it.
Perhaps studying black holes in sufficient depth (pardon the pun) will allow us to finally unify QM and relativity.