Two thoughts:

1. Does the ground there ever freeze in the winter? Probably not, but where I live, foundations need to extend below the frost deptg.

2. What weight can the undisturbed soil bear? Even if you aren't fighting frost heaves, stone walls are heavy, and over time, problems can arise. It might be worth pouring a concrete footing to better distribute the weight.

In both cases, perhaps consulting a structural engineer familiar with your local environment would be in order.