Yes, that has been the main line in public discourse and court actions, people screaming that the electromagnetic waves are disturbing them (again, the meter communicates with the operator via the grid's own electric cables, so there are no more 'waves' than before). Flat-rate tariffs still exist and are the default option here in France.
Is that really the main line, or is that just the media smear being used against a majority who have fair concerns, such as privacy or a move to phase out fixed-rate tariffs? This Wikipedia article has a good summary, and while the "Health" section is bullshit, the rest is mostly valid points https://en.wikipedia.org/wiki/Smart_meter#Opposition_and_con...