Yes, 9-1-1 is local. So calling 9-1-1 will get you the PSAPnear your present location and not necessarily where the incident is taking place.
But determining the proper jurisdiction is a routine task performed many times every day at PSAPs worldwide. Most 9-1-1 staff are not sworn police officers and as such speaking to one of us is not the same as making a formal police report. We simply work to put reporting parties together with the responsible agency.
If you call 9-1-1 on a cell phone the call very well may be answered in a neighboring jurisdiction if your cell phone is getting its strongest signal off a cell tower in that other jurisdiction. The answering PSAP simply transfers the call in accordance with established local procedures.
Occasionally a call is received as the OP posits, from far away. Suppose a mother calls 9-1-1 in Kansas City, MO and says she got a text message from her daughter living in Sacramento, CA saying she is being beaten by her husband right now. The Kansas City PSAP should make efforts to determine the proper PSAP for the Sacramento area and guide the caller according to local procedures by either transferring the call directly (if possible) or by providing the proper contact number for the correct jurisdiction.
It can be difficult to find a suitable number to transfer a call to. Mostly recently I had a caller on our little Caribbean island reporting a medical emergency and needing an ambulance dispatched in Hungary. The only number I could find on the internet was their local version of 9-1-1 so I had to call the Hungarian embassy for assistance. There is a way to make it work.