While the station might be owned by someone other than Amtrak. Amtrak general own the platform at the station.From the article: "The train would stop at existing stations along the route, such as Santa Barbara, San Jose and San Luis Obispo. This would require agreements with stations’ owners, which vary by city."
Amtrak does not play well with others.If the city or county owns & manages the station, they'll probably be reasonable. But if it's Amtrak...well, back in the '90s there was a short-lived weekend passenger service between Houston and Galveston called the Texas Limited (which operated over UP/ex-GH&H). They initially operated out of the Houston Amshack, but Amtrak got so greedy that they found it cheaper to build their own station a few miles west in The Heights (ex-MK&T trackage, now gone)!
Galveston TX to Houston TX that a city pair that could use train service. DMU hourly or better.