Why doesn't rinsing mussels with tap water kill them like soaking does? I know running water over mussels takes very little time, compared to soaking them, but the water is still entering the mussels.
For example, see this quote from Knorr UK: How to Clean Mussels:
Keep the cleaned mussels under the running water. It’s really important that the water stays moving over the mussels, but that they’re not soaking in it. If you leave them soaking in tap water, they’ll die and that’s not what you want.
This other quote from Serious Eats: How to Clean and Debeard Mussels implies that some mussels should be soaked--does soaking kill them or not?
[F]arm-raised mussels are held in tanks prior to packaging and shipping, which means that the purging step—soaking the mussels in clean water until they spit out impurities—has already been done for you