I suspect that that claim comes from the fact that cannabis is taken in by smoking, but cigarettes are a much worse problem for inhibiting healing.

Smoking does a number of things to people's hearts, lungs and vascular systems, as you know. Both cigarette and cannbis smoke present a temporary challenge to the lungs' ability to take in oxygen, which is why the heart speeds up (trying to get more oxygen transported since the smoker is inhaling smoke instead of clear air) and why, at first before the active ingredients kick in, blood vessels constrict.

That constriction occurs even at the smallest vascular level, the capillaries. And for healing of a wound to take place, capillaries must branch out and find each other, knitting/mending themselves together to bring the tissues back together. So that is where that claim probably comes from. Smoking of any kind impedes that capillary-mending process.

My hunch is that cannabis isn't nearly as big a detriment to healing as tobacco. Nicotine downright halts that capillary-mending process for a time. Which is why surgeons who're scheduling people for elective surgery will insist that people stop smoking cigarettes, ideally for a minimum of three weeks beforehand.