Does it? He was stronger than other men, but does that mean he was supernatural? The story is just like "Beowulf was incredibly strong!" They didn't need any explanation for it. That was just how he was.
Most greek heroes DIDN'T have extraordinary strength, and sure, their heroes had god blood. So did their kings. So did their politicians. So did a lot of people. The constantly had people who claimed lineage with great heroes, who had lineage with the gods, so that they could have lineage with the gods. Why? Because it gave them authority. Anyone important had god blood, because if they didn't have god blood or a god's blessing... they wouldn't be important.