Also, if you have KiCad's PCB Editor in "High contrast mode" ("Show inactive Layers as Dimmed"), then the snap is also limited to the layer you are currently working on.
Just a note for the folks playing along at home:
In Kicad 6.0.1, this mode is set by:
View -> Contrast Mode -> Inactive Layer View Mode
and a check box will appear on the menu item when that mode is enabled.
Alternatively, in the left-hand icon toolbar, it's about half-way down, looks like three traces with a via in the middle of the middle trace.
I accidentally enabled that mode and spent a few moments trying to undo it!