I think this might be related to the lack of a vertex at the spot you're trying to snap to. It may have something to do with the map projection (and hence, the curvature of the Earth), which in turn causes the unexpected occurrence.
In my example picture, we tried snapping the point feature to the line edge (where there wasn't a vertex) and got the selection cursor, the vertex cursor, and symbol of the feature all in three different locations. However, if we snap to a vertex on the line, all three show up at the exact same spot. We were zoomed in to where there is less than a millimeter between the point and the line in the screenshot. I guess if this is a limitation of map projections and the curvature of the Earth, and it is causing you problems elsewhere, then to remedy the situation, it would be necessary to only snap to vertices and not edges.
If anyone else has other information about this, please feel free to correct me.