Were they actually teaching their kids to ride without stabilisers? Or teaching them how to develop their skills? Not quite sure from your wording.
Our Saturday club has become a bit of a mecca for parents who have heard about us teaching kids to ride and we have a pretty good success record - not failed with one over the last 10 years. What helps is that we have a good, safe, cycling facility with a half-mile cycling road circuit, the use of a couple of all-weather socccer pitches (rolled shale/grit), a mini bmx track and a fair bit of grass including short slopes.
We've taught so many this summer, I sometimes seem to be surrounded by the ankle-biters bike club.
It's easy to forget that there is a "lost" generation of parents who were probably the first one to be stopped from riding generally "because the traffic is dangerous", so the knowledge which we take for granted (drop-out safety tabs - grrrr anyone?) isn't there. Many of the early questions I was asked by parents (who are required to be present at the sessions and help where necessary) brought this home to me and changed the way I thought about how we ran the club.
Even simple things like the barrel adjusters on brake levers on mtb and bmx bikes were a mystery to many, so make sure you don't take your own carefully gathered expertise for granted.
By the way, we're all volunteers - no professionals here.