Do you have any evidence, citations, experience, etc., to support this assertion?
My outboard motor (Old Johnson 9.9) stated in the manual to never run the engine without water. It also said to replace the impeller yearly.
To support the other point of view. As a kid we had a Johnson 90 and in the spring I'd always start the motor and shut it down soon as it fired. Just to make sure it was going to run. I don't recall anyone ever changing the impeller in all the years we had the boat. Which were many.
There are recommendations and there is also reality. It just comes down to how conservative one want's to be. (On my 9.9 which I replaced the impeller when I bought it, I never ran it without the muffs on. Older age = more conservative? Who knows.)