Fully qualified ski instructors are allowed to take clients off-piste for instructional purposes but they are not allowed to take people on glaciers. In order to do so they have to complete a mountain safety course as part of their training that covers:
Snow and avalanche risk assessment
Off-piste skiing technique
Equipment for touring and off piste travel i.e. skinning/snow shoeing
Map reading navigation and route selection
Objective hazards and emergency procedures
Leadership and conduct of a group in descent
There have been off-piste accidents in the past where ski instructors have been found to have been negligent, so in 2012 the Syndicat national des moniteurs du ski français in conjunction with the local judicial authorities produced a DVD detailing their responsibilities regarding off-piste instruction, which was issued to all the ESF instructors. So your man should be fully aware of where he can and cannot safely take you.
Skiing down that couloir (we use the French term
http://en.wikipedia.org/wiki/Couloir) accompanied by an instructor will have been a lot safer then skiing down the Swiss wall which is supposed to be one of the most dangerous pistes in the world. The "slab" you mentioned looks like a cornice
http://www.fsavalanche.org/encyclopedia/cornice.htm you were right to be wary, but the location didn't look ideal for explaining to someone why the lip of the cornice wasn't going to break off and trigger an avalanche which would sweep you all to your deaths especially when he was giving a group lesson at the same.
Snapzzz wrote:
What he has done is give a class off off piste newbies a sense that areas that 'look' like this are perfectly safe.
All he has actually done is give some newbies some instruction in off-piste skiing technique in terrain that he considered safe on the day, next week he might make a different assessment.
The ESF doesn't have any relevant insurance, it doesn't need any. It is owned the Syndicat national des moniteurs du ski français (SNMSF) one of the French ski instructor's trade associations, it simply takes the bookings and does the paperwork, but the individual ski instructors who are self employed all have liability insurance. Because of the way it's set up it doesn't have to levy VAT or pay corporate taxes which gives it a considerable advantage over the commercial ski schools.