KK is this perhaps another area where we have all been left behind by the modern, enlightened way of doing things! You are over qualified etc., but how old are your qualifications, how long ago were you an active gymnast (not questioning your competency at all). Is there not a parallel with so many professionals that we adhere doggedly to the 'old ways' of doing things as the best way of doing things? When I was at University ........
I do understand your concern that children should be taught how to protect themselves from injury but perhaps the 'modern way' is firstly to encourage fun and participation before being introduced to the more serious stuff.
Rather than challenge the people concerned with your perception of best practise it may be better to take a more reasoned approach "everyone is having such a good time what are your thoughts about the children's personal safety training and availability of first aid?" Either that or ask a current teacher of those training to teach about the current best practise.