Just to add:
Galen claims to have dissected about 30 human bodies in his various writings, if we tally them. Most notably there is the tale of him dissecting bodies washed out by a storm. However, Andreas Vesalius challenged these claims when he found multiple errors in Galen's anatomy. Now Galen also reported dissecting pigs and apes, so Vesalius put a human skeleton next to that of an ape, or a female dog's genitals next to a humans, and could thus show how Galen had extrapolated one to the other. This has led to the modern claim that "Galen didn't dissect any humans" in spite of his own claims to the contrary.
Now Vesalius himself made a number of errors, such as continuing to multiply the lobes of the liver, and he certainly did dissect humans, and far more than Galen had claimed. So I don't think this sufficient grounds to discount Galen's own statements completely. Before modern embalming techniques with formaline and so forth, bodies rotted quickly. Taking into account transport and the difficulty one had in obtaining corpses, it is no surprise these early anatomists made such significant errors.
Galen was also asked by Marcus Aurelius to accompany his Germanic campaigns, but managed to evade this. He was later sorry he had done so, as Marcus Aurelius had allowed some of the accompanying doctors to dissect German corpses. Limited dissection did occur. I shall look for the original texts when I have time, but I have family responsibilities at the moment.
You should also remember that there was probably a medical rivalry between the Empirikoi, who said all you needed to know could be found out from observing the living, and the Logikoi, that examined corpses and other living things to extrapolate to humans. This can be seen in Celsus, who wrote of the rivalry, and this has been implicated in the decline of dissection following Herophilus' day (In fact, Philinus of Cos, the founder of the Empirikoi, had likely been a pupil of his).
Anyway, I have attached an interesting article related to the decline of dissection, which explains both this rivalry and societal taboos as to impurity, and why the situation during the Alexandrian height of dissection and thereafter was not markedly different, that no legal prohibition has been recorded in Ptolemaic Egypt (as after all, they still mummified, which largely amounts to dissection). This is similar to my before mentioned lack of evidence of Roman legal prohibitions of the practice, but sometimes even reputable article writers repeat this common fudge, instead of actually looking at the Roman sources and lack thereof. It is thus a very similar situation to the claim that the Mediaeval Church had done so, which is also an error some reputably mediaevalists fall into, as you well know.