Here's my report! OK, woke up this morning and before jumping in the truck to head out to work, this topic sizzled in my head! OK, I'm strange I know, but with my job, these kind of things are welcome diversions!
Anyway, I simply took a bucket, no lid, and attempted to feed a hose directly into it ... well ... after the first 4 feet I couldn't shove any more in. It wanted to kink up and it simply too stiff (and used one of my older, softer hoses at that laying in the yard. I think something like this would work, IF the inside of the bucket had some kind of revolving thing the hose actually wrapped around (like a hose real for your house). We will never know what was actually INSIDE that bucket the OP saw that made it possible to coil up, but I definitely do know, this does not work just by shoving a hose in a bucket. The theory is a good one though. I'll keep working with this! This would be a great solution as I always carry about 200 feet of hose with me all the time when camping, for those times (you just never count on!).
My report... Myth Busters! BUSTED!