That is incorrect. On-campus employment is allowed in the student visa and graduate student appointments are typically RA positions which qualify as employment under this definition.
CPT and OPT are interesting cases for collective bargaining. Not my area of expertise. However, I found a different answer that seems like a more concrete protection regardless of labor classification:
> The U.S. Citizenship and Immigration Services (USCIS) cannot ask you questions about your union membership or participation in lawful union activity. In addition, the Department of Homeland Security (DHS) recognized the importance of enforcing labor laws and signed an agreement with the Department of Labor (DOL) that states it is essential to ensure proper wages and working conditions for all covered workers regardless of immigration status. It is your right to belong to a union and being a union member cannot affect your visa application.
