For a Part 121 operator no doubt about it. They also would have to have an approved weather reporting source, typically a station agent at a place like this.
The interesting question: Does the on-demand 135 operator need some sort of FSDO approval to fly into this airport? The airport is important to the town of Ridgecrest. In fact, I am surprised it doesn't have automated weather by this time.
We were in Jetsteams under a 135 certificate at the time still. Don't know if it would be different unscheduled.