A Vox article says:
Many people conflate all these under the heading “wet market.” But there are gradations here, and they represent different levels of risk for zoonotic diseases (those transmitted from animals to humans). There is some zoonotic risk anytime live animals are kept in close quarters, but the danger may be especially pronounced with wild animals; their pathogens are ones to which we haven’t had the chance to develop immunity.
They actually link a paper and another article of their own in support, but neither seem to contain undoubtable evidence that wild animals are more dangerous to us than domesticated ones zoonosis-wise, even though the claims seems a bit intuitive. The issue is that "had the chance to develop immunity" is meaningless unless the pathogen can jump species, which only happens with some mutations in some species that have e.g. (for viruses) cell receptors similar enough to ours; most viruses that can infect plants, insects etc. just "pass through" us. So we might spend ages next to some species and never get any disease [directly] from them. (I was going to give crocodiles as example of the top of my head, but that would actually be wrong.)
On the other hand, MERS for example came to us via dromedary camels, which are technically domesticated, even though the virus might be of some (more distant) bat origin. (In fact some more benign coronaviruses are suspected to have come us via camelids; e.g. 229E--a "common cold"--has "cousins" in alpacas.) And a bunch of influenzas came to us from pigs and poultry. (Deciding on zoonosis vs anthroponosis is not trivial for distant events; some researchers argue we passed the 1918 flu to pigs rather than get it from them; 229E in alpacas is similarly in doubt as to the direction of transmission.)
Of course, a better argument perhaps is that we can avoid/limit contact with wild animals, but not so much with domesticated ones. But that issue aside, is the bold claim true as written in some quantifiable sense?