Give him some credit
There is a tremendous amount of speculation here.
People have crossed the oceans in all kinds of human-powered watercraft more and less ridiculous as this one. This bubble does not look much less seaworthy than some kayaks. And its crazy looks make it immediately likeable.
Given that he made it 7 miles offshore (and 40 miles in an earlier attempt) it's clear that he had water and food somewhere. Instead of having items bouncing about in the bubble or them in the rim would be silly though, I would have gone with a towboat. (There's no boat to be seen in the story's picture.)
Navigation's trivial with a hand-held GPS. And apparently he also took a radio or satphone.
He shows up in the results database of the 2010 and 2012 Badwater Ultramarathon (200km across Death Valley in the middle of summer), so he does have some serious endurance credentials. (The site lists him as a US resident.)
So he's not completely crazy. Although I agree with the coast guard that, considering the risk of flooding to weather or a puncture, he needs a seaworthy craft at his side.