Kevin Vallier tries to sort it out:
On Hayek’s view, the UBI is required as a condition of democratic legitimacy within the framework of a social contract. I’m not saying Hayek is a social contract theorist, but he sounds like one in this passage. In order for a democratic government to be legitimate it must treat people as equals by imposing only abstract rules on them. Government gives no one special privilege, and this requirement is compatible with providing them with means to secure basic goods and services.