No, Saitama's attitude (and the comedy that brings) is not the result of how he got his power. It's a result of being unmatched. How he got his power is irrelevant to the comedy that ensued in the rest of the show, with exception of Genos wanting to know about it.

Even if he was actually from an alien planet and got sent to earth in a capsule, if he is that OP, the rest of the story stays the same.

If you disagree, please site specific instances (like I said, excluding Genos) that invalidate the parody aspect of the show if you change Saitama's power origin.