I take the view that the reason freedom of speech is important at all, is that people can be convinced to act in certain ways by speech — if it couldn't lead to action, no dictator would fear it.
We, all of us, take things on trust. We have to. It's not like anyone, let alone everyone, has the capacity — time or skill — to personally verify every claim we encounter.
Everywhere in the world handles this issue differently: the USA is free-speech-maximalism; the UK has rules about what you can say in elections[0] (and in normal ads), was famously a jurisdiction of choice for people who wanted to sue others for libel[1], and has very low campaign spending limits[2]; Germany has laws banning parties that are a threat to the constitution[3].
I doubt there is any perfect solution here, I think all only last for as long as the people themselves are vigilant.
[0] https://www.electoralcommission.org.uk/voting-and-elections/...
[1] https://en.wikipedia.org/wiki/Libel_tourism
[2] https://www.electoralcommission.org.uk/party-spending-and-pr...