Aladdin’s exact words were “Genie, I wish for you to make me a prince.” I always assumed that that meant that the wish merely caused a compulsion in the Genie to use his “standard,” non-wish-granting powers to make Aladdin as prince-like as possible. If he’d instead phrased it as “I wish to be a prince” then it would have caused reality to alter to give him a genuine royal lineage.