Well, first light does 500 miles in 3ms, but the connect signal needs to come back, right? So it should be 250 miles, at most? But this is just a detail.
More importantly, because it seems to assume that all other operations besides the signal actually reaching the destination are instantaneous. As you point out yourself, computers are not abstract machines, so the actual response time between the signal being received by the destination (even assuming it's just one straight line with zero electronics in between) and the destination replying is not zero. I imagine there can be a large variation between physical installations and different types of hardware, so much as to make it very hard to detect a clear 500 miles boundary.
Or am I missing something?