Semantics aside, this is a red herring. Whether you call it a "direct" democracy or a "representative" democracy, it's a governance system based on majority votes, not consent. Going through the courts is the correct approach in this case if they believed there was a criminal injustice that could not be remedied through electoral means. As the legal basis in this case is the ECHR, not Swiss law, taking this to the ECHR court is the logical conclusion.

You can disagree with the ECHR. Not every country is a signatory of the ECHR. Not every country is a signatory of the equivalent UN convention either - notably the US is also not a signatory to the UN convention on the rights of children and there are many people in signatory countries who don't seem to agree with it either. But as long as the Swiss government does not remove itself from the ECHR, it is subject to it. You can't have it both ways - or rather, you can and Switzerland does as it hasn't signed protocols 4 and 12 (pertaining free movement and discrimination respectively) and has only signed but not ratified protocol 1.