> Free movement of labour is an EEA policy which permits nationals of one EEA country to work in another EEA country on the same conditions as that member state’s own citizens. "Same conditions" includes the right to the same benefits.

Aside from the fact that Switzerland isn't an EEA member, Basic Income is not a condition or benefit of working in the country, it is (like, e.g., voting) a condition of citizenship unconnected with whether or not the citizen is working.