I'm skeptical of that. I know you can find all sorts of agreement on the internet, but I have yet to find any solid evidence.
True, the fuel pump is cooled by the gasoline, but I think the fuel pump is covered sufficiently in even a near empty tank. And remember, to avoid picking up sediment/water, the inlet sits a bit above the bottom anyhow.
And warranty wise, it just seems too risky/costly for the mfg to have such a marginal design. I'm not buying it. I don't recall ever seeing anything in the owners manual regarding this - if it was a problem, I'm sure they'd recommend avoiding it.
But I'd love to be proven wrong! (edit/add): I'm talking about running LOW, not completely running out and running the pump dry. IIRC, pumps run more/less continuously, to circulate fuel which helps avoid vapor lock (which seems to be a thing of the past - so it works?), so *maybe*, if you didn't turn off the ignition after running out of gas, the pump *might* continue to run dry, and *maybe* that could cause it to overheat and shorten its life? But I'm guessing it would somehow know the engine wasn't running, and shut off. And that's way different from running low ( a few gallons left before fill up)
-ERD50