It doesn't. Period. There are too many crazy ideas in here, all from people with no actual public safety system experience. (Listening doesn't count).
"Dual inputs" would do nothing to solve phase noise on the output. It sounds like something a messy ham system would try.
What these hobbyists are likely hearing is a patch between the two nets (possibly a hardware patch like an ACU1000, but most likely a software patch in the LPF dispatch console). What the user in Santa Ynez is likely hearing is a Service Net control station (possibly on Santa Ynez Peak) that is tied to Forest Net.
Similar to a multi-select, where the dispatcher can talk on multiple tones and frequencies at once (depending on link method), they can also link nets together. What is received on Forest Net can be processed and sent out via Service Net simulteneously, with a slight audio processing delay. If they're using control stations instead of wireline control, you'll hear the squelch tails from the inbound repeater (as the control station is programmed exactly like a mobile unit).
If we take usage into account, it makes sense and is far simpler (and a realistic answer) than some of the conclusions drawn previously. E372 would not be dispatched on Service Net.
So the next question is why? Why would LPF have a patch in place? As service net is new, it could be a way for testing on a net that would get very little coverage.
Keep it simple. It's the government.
Apparently he doesn't know. Service Net is in the Firescope MACS441-1 for 2020 which has the required frequencies for mutual aid in CA, so it should be in his radios. He needs to check current information. Is it WRA Fire?