I searched for "Arabian Nights roc carry elephant" and found Second Voyage of Sinbad the Seaman, almost at end:
"Voyagers and pilgrims and travelers declare that this beast called karkadan will carry off a great elephant on its horn and graze about the island and the seacoast therewith and take no heed of it till the elephant dieth and its fat, melting in the sun, runneth down into the rhinoceros's eyes and blindeth him, so that he lieth down on the shore. Then comes the bird roc and carrieth off both the rhinoceros and that which is on its horn, to feed its young withal. "

The roc carries a rhinoceros who has an elephant impaled on it horn to feed its young. So Shanks understated, rather than exaggerated, the payload of the roc.