That local psychiatrist turns out to have served two purposes.
The clinic asked me to meet with said psychiatrist so as to
give "clinical context" to admissions about me, which was done.

Turns out the other way that the psychiatrist was important,
was to contact my insurance, as a provider, and to help insurance determine
how much I needed treatment.
The letter (from the clinic) was formally delivered to me this week,
saying that the insurance would accept the treatment thing.
This means a high deductible and subsequent co-pay.
Without the psychiatrist contacting my insurance as a provider,
I'm not certain how acceptable the insurance would have found this.

So that is good news.
Oh, the shower -- somebody finally solved the mystery.
The thing that determines cold and hot water, and the mix, in the shower,
was installed backwards.
When that happens, the lever cannot just be adjusted the way one does, by turning to hot water and then easing away from it in order to include enough cool water so as not to get burned.
In this case, you have to stand there wiggling the lever back and forth, back and forth, back and forth, and eventually
the shower will cough up some warmth --
but not with the lever in the conventional hot-water position ...

it seems like a dirty trick.
I guess it's just what happens.