This means that even if you’d end the EU, these same people would still be able to pass the law.
If a controversial law is proposed in a national parliament, then it becomes big news. A politician pushing an unpopular agenda would eventually find him/herself voted out.
But average people don't usually hear about laws the EU is creating until they're implemented. Hardly anyone had heard of the GDPR until it was too late. And the whole legislative process of the commission is opaque: you can't tell who in your government was responsible for supporting a particular position.
Instead, 4 years later, the same national politicians that wrote the law blame it on the "undemocratic" EU.
You're absolutely right about the media.