Michael Cox wrote: "Lots more water than you think they need". And theirs were seriously impressive. Have you the possibility of trying a side by side test? One patch watered and another not?
I don't have running water. The first year at this property I hauled endless buckets of water for my squash. They did well, for the conditions I was working with. The next year, one patch got a bit of water and one patch got none. I saved seed from the plants that did the best with little to no water. After that I stopped watering altogether. This is my fifth year growing squash here and my unwatered squash this year look better than the heavily watered squash the first year. They're way bigger and greener than the naticoke landrace I'm trying out from the experimental farm network, so I don't think it's just the improvement in the soil over the years. I'm too lazy to haul water now that I know I don't have to ;)
This year I'm also growing squash in completely undeveloped areas - areas no same person would rely on for food. They're small and struggling, but one plant in particular has two fruits on it already, same as most of my squash in beds.
I've heard that dry farmed melons taste better, which is the main reason I (try to) grow mine with out water. I don't have the room yet to focus on more than a couple main crops each year, so melon development has been neglected. I have a couple problems leading to fruit set too late in the season, that I need to devote some space to to work out of the genetics.