> I ASS-U-ME that there has to be some kind of isolation in a UPS unit. Is that correct?
No.
Sluckey may see it different, because his shop works with high-end gear.
The $69-$499 UPSes mostly pass-through when not on battery.
One affordable brand had buck/boost to keep you near 120V with 100V-150V out of the wall.... but if the input was ugly (or UN-grounded) the output was still ugly.
The on-battery output of the affordable UPSes is VERY ugly. Near-square-wave. Actually worse: it pauses at zero twice a cycle so that both the RMS (lights) and the peak (electronics) are similar to nominal sinewave values. In addition to all the harmonics of a squarewave, there's another overtone series. This may be modestly filtered, but is still worse than about any wall-outlet unless it is overloaded with SCR dimmers. (I used to work next to large dimmers and it need not be a problem.)
> wall simply connects to the rectifier
That's a high-end UPS. Critical-mission stuff.
> benefit to using a UPS?
You can play in the dark?
Same as the laser-printer: you "can" buy a UPS to hold-up anything through any failure. But for a gig, or a print-out, it is usually better to wait until the power comes back.
I did know one stupid reason to run audio on a UPS. A guy had a TV set which remembered the last volume setting. But forgot after a power-loss, and the default was LOUD. And his power blipped a lot. He ran just that set on a UPS just to hold the volume setting. It would have been better if the TV designer had made better choices, but what can you do?
Many UPSes also have line-grounding diagnostics equivalent to the $8 tester.