As Gen mentioned, it's up to the vet (or shelter) to scan for the chip. Many say they do scan new patients, many don't for the reason she gave.
One thing about chips, there are several different manufacturers. Some require their own equipment to scan them. I would ask about a chip that is scanable with a universal scanner.
I'm no expert, but to me the best solution is a GPS collar with an unlimited tracking option. Some of the collars that I've looked at had different options for the number of GPS 'pings' that it allowed on the contract. That is, once every 30 minutes, once every hour, or unlimited by-the-minute pings. The best service option I saw was one where you can access the collar with your cell phone and know where to look for the dog with unlimited pings.
A company called Rakon in New Zealand has produced the smallest GPS chip so far, it's about the size of a human baby's fingernail. The chip isn't the problem, it's what to do for a power source for an implanted device.
Pet GPS collars aren't cheap. This one starts at $250, and I'm not advertising it, it's just here as an example.
https://www.spotlightgps.com/gps-pet...g-devices.aspx