... legal responsibility that specifically says 'even if it's our fault'?
Haven't got much experience with litigation happy countries nor flight, but the indemnification clause is pretty universal coverage. Maintenance costs are high in any vehicle and if the clients can foot the bill, all the better for their profit margin (and possibly safety in the long run).
https :// aboveaviation . com/liability-waiver/
http :// aerowoodaviation . com/site/wp-content/uploads/2019/05/2019-3-11-Aerowood-Introductory-Flight-Waiver-and-Release-4844-2587-4824.pdf
But then, whether such a waiver might hold up in court is dubious.
https :// www . pilotsofamerica . com/community/threads/liability-waiver-for-flight-training.74611/