Many comics embellish and exaggerate, but most of the comics I know feel as I do that this is over the line. He's lying about real people, and making up anecdotes for more than comic effect -- getting audience reactions and sympathies with stories he made up.
Listen, if the audience understands that the stage "Hassan Minhaj" is a fictional character who entertains with fiction, then fine -- embellish away. But I think it's clear that his art kind of requires it to be true.