And those skeptics would be both right and wrong.
Wrong in the sense that the antidepressant effect of ketamine lasts for some time after the drug leaves the system, so we know it's not just a temporary drug-induced effect.
But somewhat right because the antidepressant effect isn't very durable, so it's mostly useful in emergency situations (suicidal tendencies) and for kickstarting conventional therapy. Even the rare patients who convince their doctor to prescribe ketamine multiple times per week over the long term usually encounter diminishing effects as tolerance sets in.
Unfortunately, the high relapse rate presents a huge conflict of interest for these ketamine clinics, which are often more than happy to continue taking your money in exchange for ketamine sessions. The more ethical ones will insist that patients be enrolled in therapy and will educate them on proper maintenance antidepressant options if they choose. The less ethical ones will give patients a speech about how traditional medicine is bad and their only real option is to continue coming in for more ketamine.
There are some horror stories from one of the local ketamine clinics here. I'm actually shocked they aren't more tightly regulated at this point.