We do the latter, and I was parent teacher. Not a volunteer position: our preschool dues are lower because I worked in the classroom, in a sense it's a "paid" gig.
We had a very relaxed attitude towards personal harm. Getting hurt, crying, and getting better is part of the learning process. Not to say that we excessively allowed kids to get hurt, or allowed them to engage in explicitly dangerous activities, eg: throwing things, hitting kids.
But I did supervise some kids who wanted to "wrestle" and "fight"... I took it upon myself to teach them to "fight clean" and when people were down we would call a break and let everyone stand up and try again.
Also the prechool was mostly outside, and kids got dirty. Oh yes indeed, the mud pit was very popular!
This all btw is in San Francisco.