Are you sure he never claimed it? I beleive people called him World Champion including Edge at the end of his book - I would need to double check this.
Did Morphy explicitly say he wasn't world champion? Or do we just not have anything recorded one way or another.
It seems (if wikapedia is to be believed on this, that he was often introduced as the world champion.) If I was introduced as the Bishop of Rome I would probably correct that introduction at some point. Did Morphy ever correct people when they called him World chess Champion.
The only instance that I recall off-hand of Morphy being, not actually introduced but noted in a speech, as "Chess Champion of the World," is by Martin Van Buren's son, John, at Morphy's victory reception at the NY Chess Club on 3-25-1859. I can't recall Edge calling Morphy, or refering tto him as, a World Champion, but, if so, maybe you can give it. At the end of his book Edge said, " Surely, it is not too much to declare, on the authority of so much proof, that Morphy can give pawn and move to every living player."
Morphy isn't recorded anywhere that I know of to have claimed any title (except perhaps that of American Champion by virtue of winning a Congress established specifically for the purpose of finding a national champion), though it seems he proved to his own satisfaction that he was, indeed, the best player in the world. Most of the world seemed to agree. Still, there's a difference between being the best player in the world and being World Champion.
Morphy never said he wasn't World Champion, but why would he? I can't think of any sport that had World Championship at that time and, while the concept doesn't seem completely nonexistant, it was certainly very shadowy and unformed.
The only known potentially serious challenges to Morphy whom Morphy didn't play (during the time he was active) were possibly Petroff in Russia and v.d. Lasa in Germany. Judging from Morphy's manhandling of Anderssen, even those two players weren't likely to have put up much resistance. Some people have suggested S. Dubois, but that would have been dubious or perhaps Duboious.
Love the pun ^_^