Wow, this is quite the video. Very sad stories. I have a few thoughts -
Some of these instances are oral surgery (OMFS) based as previously discussed. At my residency program they were with us 3-4 months and act as a CA-1, and get about 2-3 weeks of "pediatrics" (outpatient only) experience - they are pretty high level individuals as it seems very competitive to get in (some have a mix MD/DDS or DMD degree, some just DDS). But I wouldn't trust them doing anesthesia independently as an anesthesiologist (they didn't even finish a full year of training), and I would be even more concerned with them inducing general anesthesia and then turning around and doing surgery on the mouth with only a sedation nurse to monitor vitals - do they follow ASA standards, including ETCO2? I don't know, but I wouldn't be surprised if they don't.
So that is an issue. The other MUCH more troubling aspect is that pediatric dentists commonly induce deep sedation (or let's be honest, they probably do the "room air general" technique with oversedation) in their office. To my knowledge pediatric dentists don't do anesthesiology rotations like OMFS and thus aren't trained with administering general anesthesia, at least the training programs at the hospitals I've worked at haven't. That is absolutely terrifying! Just listen to that report on the first child who had anoxic brain injury - sedated with nitrous, "anti-anxiety" (likely Versed, but possibly Ativan/Valium) and Demerol. And this case was within the past two years. Terrible situation all around.
For what it's worth, the practice I'm joining after fellowship actually covers a couple dental offices for general anesthesia cases. I'm not sure if it's OMFS or general dentistry.