That's what they claim, but in reality the President of the Commission rejects any Commissioner they don't like. This isn't meant to happen but eventually Juncker admitted that he did it all the time, and that this was considered normal.

So the Commissioners are in reality selected by the President.

This problem appears in every HN thread about the EU or its activities. People argue that it's a legitimate democratic structure based on how its treaties say it works, but the treaties aren't followed.