I was going to hammer him on the energy content of one gallon of water, but it turns on gallon of water has 0.42 kg of hydrogen which will yield 16.7 kWh when recombined with oxygen (either by burning or in a fuel cell). That's a little less than my daily average and some (or a lot) will be lost to inefficiency, but at least it is in the right ballpark. I still disagree that a credit card sized solar cell will receive enough sunlight to do that conversion in a day unless a lot more light is focused on it.
I suspect some Clintonesque parsing on the good doctor's part.
He says "Placed in a single gallon of water in a bright sunlight, the device could produce enough electricity to supply a house in a developing country with electricity for a day". Parsed exactly, his claim is that his device will get enough energy from that gallon of water to power a house for a day.
He does NOT claim that his credit-card sized device will PRODUCE that energy IN a day's worth of sunlight. If his credit-card-size device takes a couple of months of sitting in sunlight to produce enough hydrogen from that gallon of water to power a house for a day, then his statement is still technically correct.