Absolutely not true. Most personal gear is off the shelf standard outdoor gear - REI, Cabelas, Campmor, etc.
There is the issue of specialized items - Stokes and SKED litters, extra long (600') ropes, radios, pagers - those are typically purchased and owned by the organization, not by the individual members. YMMV
You raise an interesting question. How much did I, or the typical member, spend on SAR, beyond what would have been spent on outdoor goodies anyway?
Not very much, in my experience. I did have three kids to educate and put through college, so I did not have unlimited funds, but I don't recall any inordinate strain. I did buy a rather expensive Marmot down bag, light and warm, which could be configured as a double bag if necessary. I carried it on some operations, but I have used it on many more personal trips. Twenty-five years after I purchased it, it is still in service (Real quality gear has a very long service life.)
My most useful stove was a light, cheap Trangia (still available today). I recall fondly a cheap acrylic zippered sweatshirt from Sears that cost, like, $13 - a versatile, useful item.
One of the issues back in the day (70s and 80s) was finding decent, dependable lights. Today, I am amazed at the proliferation of dependable,light, bright LEDs that outshine anything available back then.
One other thing. If I wiped out something significant on an operation, in my setup at least, I could always submit a bill to the Sheriff's Office for reimbursement. This was rarely necessary.
I agree that a donation to your SAR unit would be highly appropriate at this holiday time. Even better, both for you and the unit, would be to also donate yourself.
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Geezer in Chief