"All vertebrates have similar physiological pain receptors ." This might be true, but doesn't really decide the issue. Pain receptors are in the peripheral nervous system, but pain is mediated by the brain. In humans, there are many cases where we have activation in pain receptors without consciously feeling pain (soldiers during battle), and similarly there are many cases where we consciously feel pain without any activation in pain receptors (phantom limb pain, chronic pains). Also, it's worth noting that the link you provide refers to a table in Gary Varner's 1998 book. I'm a former grad student of his, and I don't think even then he would have said the argument for pain is "just as strong," in other groups as in mammals, but he does have an updated table in his 2012 book "Personhood, Ethics, and Animal Cognition" that incorporates some of the points I mentioned above. And, in particular, he writes (p. 123) that "...the argument by analogy for pain in non-human animals is strongest in the case of our fellow mammals, and weaker for all of the other taxa." He does still conclude that the best place to draw the line is between vertebrates and invertebrates, but he's also not saying the arguments are equally strong in al cases.
Though I think that fish and chickens probably feel pain, and that we certainly should base our moral decisions on the assumption that they do feel pain, it also seems pretty clear that there is a stronger argument by analogy in the case of mammals. In particular, the anterior cingulate cortex and the insula cortex play a central role in what is known as the affective dimension of pain in humans and other mammals. The most striking evidence for this is that humans with lesions to these areas will report "feeling pain but no longer finding it unpleasant," but there also is extensive evidence from fMRI on humans and other mammals, single-unit recordings on humans during surgeries (and on other mammals during invasive research), direct stimulation (in the case of the insula) on humans and other mammals, lesion studies on other mammals, and knock-out and knock-in studies on mammalian brain structures.
This is relevant because all and only mammals have these brain structures (the cingulate and insula). There aren't any particular behavioral responses to noxious stimuli that you would see in, say, a mouse, but not in a chicken, which is why I think we should assume that they also consciously feel pain. Nevertheless, it is pretty clear that saying "organism M probably feels pain in a manner similar to humans because M has all of the same brain regions which seem to be doing the same things during noxious stimulation and M also has behavioral similarities" is a stronger argument by analogy than saying "organism M probably feels pain because it has behavioral similarities to humans." So even if the best place to draw the line is between vertebrates and invertebrates, we shouldn't confuse that claim with the claim that the evidence is equally strong in both cases. Whether the evidence is strong enough to outweigh the large difference in numbers between eating beef versus chicken, probably not, though I'm not exactly sure how to weigh the "probability of similarity" from arguments by analogy.