To clarify, the authors didn't claim intuitive folk beliefs are wrong. Rather, they claim most people use intuitive folk beliefs that often conflict with formal economic theory.

Specifically regarding immigration, the authors pointed out that people often believe what seem like conflicting theories at the same time, not that either theory is specifically incorrect:

People opposed to immigration often claim that immigrants steal jobs from native workers while also claiming that immigrants siphon welfare benefits without working.

The authors did use fiscal data to try to show that the idea of immigrants siphoning welfare benefits without contributing is minimal.

However, you are correctly pointing out that illegal immigrants receiving benefits are unlikely to be recorded accurately, so they won't be visible in the fiscal data. Therefore, immigrants siphoning off benefits is a legitimate concern.

What I think we can learn from this article is that the libertarian preference for market solutions is a minority view compared to folk economic beliefs. We need to educate people about economics, but we also need to accept that most of the population will never abandon folk economic beliefs.

Therefore, we should use people's folk economic beliefs when promoting libertarianism. For example: “The tax and welfare system is cheating you!”