What your lawyers said sounds believable. It has absolutely nothing to do with "right to work" laws, which are a particular legal concept that have to do with union fee requirements. A quick google search suggests that there was a South Carolina supreme court ruling about noncompetes that addresses "the right of a person to use his talents to earn a living", so I can see what your confusion might stem from, but this is distinct from "right to work", which is a sort of political/legal shorthand for something specific to union contracts.