What should a working professional do if a prospective company or employer advises them to do an internship or a fellowship, but they have graduated from college five years ago, and already have done multiple internships and paid employment?

I attended a virtual career fair for public media (e.g. public television and public radio affiliates in the U.S. - PBS and NPR member stations). The employers represented there were telling me to do a fellowship and were suggested it multiple times. Others said, to do an internship. I currently work full-time (full-time employment) at a news outlet. This is my second job in the industry. I previously worked at another news outlet. What does it mean when a prospective employer continues to tell working professionals and job seekers to do an internship (s) and/or fellowships (s)? What does this say about them, especially public media? What should us working professionals do? I do not feel like I should attend any more career fairs with public media because they say this to people every year. Thank you.