The study lists eleven specific claims that were tracked, all objectively false, six of which were primarily shared by conservative users and four primarily shared by liberal users.

That was my first thought too but I looked at the list of claims. They're all very US centric and I hadn't heard of any of them, but none obviously jumped out as true but rated false. There was one about a fabricated quote assigned to a US politician, and I couldn't find any original source for it (and it was suspiciously extreme anyway).

At the very least if one was incorrectly classified you'd need to do some legwork to demonstrate that.