I think the argument you quoted (and it looks like your reply somehow got attached to the wrong post) was implying that the supply of labor is unnaturally inflated by requiring people to work to eat. Basic income, the argument proceeds, would allow unwilling suppliers of labor (the "wage slaves") to drop out of the market, as they naturally would if they weren't forced to participate. There would no longer be a need for a minimum wage at that point (since all wages earned go on top of a basic income), so the supply, demand, and price of labor could reach their true equilibrium.