Who knows what he saw - but he certainly had no reason to lie. Although there is no mention of him walking anywhere or having his fleet destroyed in the Wiki on him. Just that he had 3 principle voyages as a slaver and was part of the fleet that destroyed the Spanish Armada.
Any elephants living in the mid-16th century could have been killed or died off long before settlers arrived.
The sailor I am referring to was David Ingram who was set ashore at or near Tampico, and claimed to have walked clear to Newfoundland where he, and two others, were picked up eleven months later, and saw elephants on his trip. This story is reported in the book THE DEFEAT OF JOHN HAWKINS by Rayner Unwin. Chapter 16 is THE IMPROBABLE WALK.
Ingram met with Hawkins after his return, and was summoned to several courts to hear his tale.