The flame carrier can board a ship but he/she has to keep moving on the deck. That is how the ancient Greeks intended.

I don't think the ancient Greeks could have envisioned a world where the Olympics was played thousands of miles away from Greece and included every nation on the planet.

Most likely Alexander thought of it.

A muscle-powered boat would be in keeping with the spirit, right?

If you're asking me, I think a sailing/wind-powered ship would be fine as well.

But, I agree, it takes a bit away when you have all the planes, snowmobiles, etc...