Yes and no. The hockey example applies if, say, the injured player were to sue for damages due to injuries sustained; if the injuries were those to be expected in the normal course of the rough and tumble of game (up to and including having your throat slashed open by a skate, which has happened) then the player consented to this activity and must have understood the risk, especially if they are a regular player. OTOH, if negligence or criminal activity (action clearly well above and beyond the normal game activity) cause the injury, then the player has every right to sue and the state has every right to charge someone.
IANAL - this is what I was told. In the ski hill example - just because you fall, or fail to stop and hit a tree (cue Sonny Bono) does not mean it’s the owner’s fault. However, any failure to run a proper hill can be brought up as contributing negligence - including no crash barriers to equipment, lack of warning signs, failure to properly supervise other patrons resulting in collisions, etc.
This is the same logic that applies to slips and falls in a store; you don’t sue because you fell in their store, you sue because they didn’t clean up the spill in aisle three, or they didn’t clearly mark the “watch your step” or get rid of the ice on the sidewalk. The moral of the story is that a good(?) lawyer can find something that in some way contributed even a tiny amount to the injury - the hill was too icy because you didn’t use the snow groomer - and turn that into a case of contribution to the damages and make the owner pay.
I have never heard of a life insurance policy company being able to collect from the party which caused the death. The medical insurer, maybe - for the medical costs up until death. Auto insurance would not apply on a private course, and odds are racing cars are not licensed and insured like regular cars. (The liability of an organizer of a rally on public roads is a whole different kettle of fish, I’m sure…)
There’s the legal concept of “so broad it’s meaningless” in legal / contractual terms. The waiver for skiing, for example, says something like “I understand that skiing is a sport that can contain some dangers, including snow conditions, hidden obstacles like rocks, …” . At least in Canadian law AFAIK, you can’t really sign away rights absolving the other party of gross negligence - although it may be harder to sue if the neglect is minor.
(There is also a case in Canada, based on a prenup/divorce case. The couple were lawyers; the wife signed based on the assumption “this is so one-sided, a judge will throw it out.” The judge basically said… it’s not that unfair that it’s unconscionable, and as a lawyer you knew exactly what it meant and you consented. You cannot automatically presume that a judge will negate your consent.)
Whether the Texas story is true, or simply that the damages of death are greater than those of personal injury, or what the real story is - who knows? Maybe it’s a simple as you cannot sign away the rights of your heirs to sue over your death.