Does insulating a slab on grade make the building less stable?

A Slab on Grade needs to be built correctly, but no, Insulation under a slab floor will not make it less stable. To me that sounds like someone who has built frost walls but never a slab, and builders will often express doubts about unfamiliar building techniques. That can on occasion be an effort to steer a potential client towards something that they themselves do in order to win a contract, or it may come purely from genuine concern, but it still doesn’t mean it is based on anything tangible.

A slab should be designed by an engineer based on the climate where it is to be built, the soil conditions of the building site, whether or not the building will be heated, and the weight of the building that will be seated on it. The engineer will specify what type of insulation is to be used, how much, and where it will go. With an edge loaded slab (thickened-edge footing) It would typically be high-density EPS foam, but a raft slab (which distributes the weight evenly over the entire floor) doesn’t even require high-density foam. 

To put the compressive strength of EPS foam in perspective – it is used under roads in the far north as well as airport runways in cold climates to prevent frost damage. As long as your slab is designed by an engineer you have nothing to concern yourself with.