This might sound pedantic, but I get tired of people referring to "GPS" as a mobile GPS naviation app. GPS refers to the entire system of satellites and ground stations. From this system, one can build applications on top of a GPS receiver, which provides the position. So yes, the patent troll doesn't own the satellites and ground stations.
I don't use Foursquare, just read the description of the service.
Does Foursquare use the very last step in the description?
My understanding is they update location when user "checks in", not when system detects that the user's device is stationary.