I don't think Steve Perry ever pitched down his vocals. IMO there are two types of singer, ones with good technique (due to practice or genetics) who can sing easily, and those who have to really force notes out in the studio (relying on perfect conditions) then pitch down live.
I agree he always seemed to me comfortable in that range, on talk shows, etc. The guy from Aerosmith on the other hand I would be surprised if he could match the radio version regularly in concert. As for Layla, I guess I only know the live/mtv unplugged and the original had higher notes?