In MA, it's a BLS skill for a basic working on an ALS truck, so performed under the order (and supervision) of a medic.
My default (if theres ever a problem) before immediately bagging a patient is to turn to FiO2 up on the vent-- and see if that corrects the problem. It's what we would do to a non-vented patient, who is on existing oxygen (turning up an n/c, switching to a NRB). From there, of course, transfer to a BVM while troubleshooting vent with staff/family, or preparing our vent with consultation of family/facility RT. RTs are generally an excellent resource, if available, I encourage you to take advantage of their wisdom and problem solving magic.