What are you switching? If it only takes a small current your snubber will conduct enough to appear on. You'll need the snubber on the high current triac if that's what you're driving.
We had a mystery problem once that I couldn't figure out. We had a circuit that would spontaneously fire. It was a photo-triac driving a high current triac. When we had one motor connected it was fine. When we connected up a second motor to an identical parallel circuit on the same PCB, both circuits would randomly fire when both motors were supposed to be off. With snubber, with snubberless triacs it didn't matter.
The only fix for that was to put two photo-triacs in series. The breakdown voltage was 400V on that part and we were controlling 230V. Somehow two motors was causing it to breakdown.
Anyway my point is that you put the snubbers in where you need them. You'll know about it when you do.