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It's not required on a remote power module because the RPM doesn't use the load as a neutral connection in order to power the dimmer.
When the RPM output is 'off', no voltage is available so the LEDs will not turn on.
I believe that there is a leakage current through the output thyristors. As I understand it, Lutron RPMs are isolated from power by one relay at the feed circuit. The relay opens to isolate the outputs only when all circuits are commanded off. If the relay contacts are not open, a high impedance load could be energized by leakage current even if that channel is commanded off.. Crestron CLX modules employ isolation relays on the ass end of each output circuit. If a channel is commanded off, the load is mechanically isolated from module power.
Regardless, the LUT-LBX is a low impedance device used to provide a minimum load for dimmers. Even dimmers that have a neutral connection, and do not complete their control electronics power path through the load have minimum load specs.
LUT-LBX is recommended for use with LEDs because it provides enough of a load to swamp out the leakage current, so "none" flows through the high impedance LED load.
If Lutron tech support says they shouldn't be used with RPMs, maybe they have had some sort of issue with them, even though they are spec'd for RPM use. I'd prod Lutron for more information.
Worse case, you could wire an isolation relay into the circuit. A 120V AC coil is probably low impedance enough not to be picked up by the leakage current, but also might drop out before the low end of a dim is reached.