Ugh, that's the worst! So many people just throw the stones right on dirt. You gotta dig down at least four inches and put in a solid gravel base. Compact it really well with a tamper, then add your sand leveling layer. If the ground can move, the stones will definitely sink. Skipping the gravel is just asking for a wobbly mess next spring.
But come on, is it REALLY that big of a deal? People have been putting down stepping stones forever without all that extra work. My uncle just dropped his on the lawn like ten years ago and they're fine, a little wobbly maybe but who cares? It's just a path. Feels like overkill for some rocks in the yard.