but no, the judiciary is not a legislative body (nor is the executive). it curbs legislative power through interpretation (as does the executive), as is their charge, and therefore has influence and power at the margins, not in the wholesale creation of laws. it's more influential in the negative--striking down unconstitutional laws wholesale. that's not the same as a legislative body.
besides, representative democracy centers around the legislature, not the judiciary. talking about an undemocratic judiciary was just a contrivance for partisanship.
For what it's worth, the nature of the judiciary appointed by representatives chosen by voters is just slow representative democracy. It is no surprise that, given the ability to make a law-like, appointed in a manner that is representative-like, they act lawmaker-like.
They are, in their activism, isomorphic to lawmakers. That's what judicial activism is. In a POSIWID sense, the judiciary are lawmakers, no matter what you call them, like North Korea is a dictatorship despite being called a Democratic People's Republic.
the judiciary isn't a parallel lawmaking body. the legislation has corrective oversight of judiciary interpretation (outside of consitutional issues). that the legislature only exercises their oversight selectively inconsistent to your wishes is not a judicial issue.
also, "judicial activism" is a loaded term. the judiciary is doing exactly and only what it's tasked to do--interpret law against the backdrop of the constitition; it's not a bug if you disagree with its decisions.
He's absolutely correct that American courts are, in actuality, through the precedent system and novel interpretation of law around cases, a defacto legislative body. They're sort of like a House of Lords. Examples are Schenk v US and Roe v Wade.
Overall, I think this has been effective in practice in the US, but it isn't quite in the spirit of the judiciary as you describe it.