That makes sense only if they also have legal responsibilities to go along with their rights.

Take for example PG&E, the large gas/electric utility for the northern 2/3rds of California. PG&E is a convicted felon and was sentenced to five years probation, but they remain un-rehabilitated.[0] Under your theory, the "group" with the rights should have been jailed. Instead, a new layer of rights is created out of thin air for the corporation but no meaningful responsibility was ever assigned, unlike individuals.

[0]https://liberationnews.org/pges-rap-sheet-the-criminal-histo...

PG&E is certainly a grotesque entity, no argument there. Of course, it's a government created and strictly regulated monopoly as well.