Do you think that people should always analyze their gas no matter what they "think" is in the bottle?
Yes.
Do you think that people should trust the accuracy of an unknown analyzer?
If it appears to calibrate to Air correctly and it analyzes the gas to the expected value (and which is 40% or less), I would generally trust it. But, I would always advocate being situationally aware and using good judgment. For example, if it's a reputable shop that looks clean and well-organized, and they offer a banked gas, and the analyzer they provide me is not the same one they use back at their fill station, then I would have no issue trusting their "unknown" analyzer. OTOH, if, for example, they are doing partial pressure blending and the analyzer they are offering for me to use is the same analyzer they used to do the mixing, then I might look for alternatives. In that situation, there's no way to know if their analyzer has an old O2 sensor that is reading low.
That's one reason why I carry my own analyzer with me and I check the calibration against O2 periodically.
The other reason is because I was diving in Hawaii once and the shop I booked a boat through met me at the boat with my tanks of Nitrox. They didn't bring an analyzer and the boat didn't have one (and I didn't have one yet). So, my choice was to trust their tanks or use other tanks they told me were air. I used the tanks of air (which, of course, still involved a level of trust).