Perhaps the dispatcher in the local jurisdiction where the call is placed may be able to quickly and directly contact emergency services in a neighboring town that could respond faster. (This is just presented as an example.) Living by the Connecticut River as I do, and with a limited number of widely spaced bridges, a 911 call placed in and answered by dispatchers in, say, South Windsor (on one side of the river), may be more quickly responded to by the emergency services from Windsor, on the other side of the river. So I would be as certain as I can be that the South Windsor and Windsor dispatchers have each others’ emergency services’ direct lines to handle situations like this when they arise. I’m sure there are any number of jurisdictions that have these kinds of geographical (and sometimes political) constraints, and which they have learned to deal with over the years.
But obviously the emergency services dispatchers in South Windsor and Windsor, as close as they and other nearby towns might be, would have no likely way to contact the police in East Podunk if your friend gets into an accident there, and especially if that occurs out of state. But I’m also certain that the dispatchers have their own State Police numbers on speed dial, and possibly the State Police for neighboring states (read “provinces” as applicable) as well, so the call to your local 911 operator could be quickly routed to the neighboring state’s police, and very likely state and provincial police distantly removed from one another.
I’m certain that in this day of quick interstate and international transportation, it may from time to time be necessary for the Connecticut State Police to call the California State Patrol, for example, to inform them that a fugitive is believed to be on a commercial flight due to land at such-and-such a time and place, and that a Connecticut warrant has been issued for the person’s arrest. So state police can contact each other quickly, I have no doubt. (And for a life-and-death emergency they would do that, too.)
For non life-threatening emergencies it’s probably wiser to simply look up the direct-dial number that you want instead, and place the call via the department’s number if possible.