It seems that according to the number of use cases here on forums it would be nice to have additional setting in netwatch that would limit the ping test to particular interface, or even better, a way to route-mark or packet-mark packets originating from the netwatch process.
The idea behind is that netwatch is often used to monitor load balanced tunnels or uplinks, so in these cases one needs to add specific rules to either firewall or routing to force the check ping to follow specific route