Fuel injected vehicles have a much higher pressure fuel pump than carbed vehicles. Some designs might have trouble with priming, but most these days are submerged pumps that are installed in the tank. This solves the priming problem, and cools the pump.
This is a perfect example of what is happening here--any new technology is going to have hiccups. Fuel injection had _lots_ of hiccups, that have mostly been resolved. EV is bound to have hiccups, and is bound to get resolved.
Interestingly, the same applied to some models of RX-7. If you ran out of gas, you'd potentially need a service to re-prime it.
Didn't stop me from buying one.
// Not sure if myth. Never ran out.