I think there is a difference for most people in what types of support and intervention a therapist provides vs. what a pdoc provides. I can see where the distinction is made between a "crisis" in therapy as opposed to a crisis that a psychiatrist would intervene in. That might not be so clear in cases where the psychiatrist is also doing therapy with a client, but those situations aren't terribly common most of the time.

My therapist was my go-to person for most crisis situations, not my psychiatrist. I could get in for extra appointments fairly easily, process through whatever was going on, and hopefully get through the crisis without need for pdoc support or inpatient.

I never had "crisis" appointments with my psychiatrist, but we certainly had phone calls. (Due to distance, getting in a for a "crisis" appointment was not really feasible.) My pdoc handled my meds for the most part, and in the event my therapist's support in conjunction with meds was not working and I was in crisis (suicidal; manic, etc.), then we spoke on the phone for a med change if possible, but if that couldn't happen quickly enough or the level of intervention moved beyond what a med change could correct, then my pdoc would ask me to go inpatient where he could be sure I was safe and he could make more aggressive med adjustments under medical supervision.