So by that definition, circle jerking will feed everyone.
Yes, that's how every economy works. Everyone works for everyone else and everyone profits.
I know you said they can earn the $1 off someone else and use that to buy the food from the controller of food, but there's only so much the controllers of food needs (or has time to consume), and that's the problem. Once he has all the $ in circulation, where will the more dollars come from without an army backed inflation currency?
If you worry about this scenario, then a guaranteed basic income isn't the solution. If you can't exchange your basic income for food, what good would a basic income do you? I can't imagine any realistic situation in which people would need to worry about this, but if we ever get anywhere close to it, I'm sure the superior technology we'll have in that far distant future will make possible a solution you and I could never even dream of.