Within the US, it seems similar to skydiving, to a decent extent. The United States Parachute Association is affiliated with the overwhelming majority of dropzones and their (the USPA) guidelines are followed in addition to the relatively small amount of FARs (federal air regulations) that directly address skydiving.
I'm still a fairly new scuba diver, but it seems like the USPA is ~= PADI/SSI/etc, but those are more worldwide-oriented.
Within skydiving, there is clearly a substantial assumption of risk for anyone jumping out of an aircraft, and courts have generally upheld the waivers signed by jumpers, notwithstanding gross negligence by the DZ.
If a solo, licensed (or certified, really, since the government is not involved) jumper goes in because of his own bad decision making (the most common way we die: flying a perfectly good parachute into the ground) and there's no problem with the reserve (which has to be packed by an FAA-certificated rigger), the regulators tend to say "welp" and file it under "played stupid games, won stupid prizes". Maybe it'll lead to the USPA updating guidelines if they start spotting a trend (when action cameras started becoming a thing and people started dying because of distraction or entanglements, the USPA threw out a guideline saying jumpers should have a C license/200 jumps before jumping with a camera).
However, it still causes problems. First responders have to come, resources are spent, etc. Operations generally have to cease for some amount of time to handle the emergency, etc.
On the more severe side: any time there's an incident involving a tandem student, or the aircraft itself, the FAA will come knocking and as I've heard said before: "the dildo of consequences rarely arrives lubed" and we really, really do not want to invite more regulation to an activity that has remained remarkably free of it, all things considered.