If these are the only two options, and if fallible human beings today have no way of avoiding their ideas and beliefs being in the latter category, then surely young earth creationism must be false.
First, having made claims which have been so definitively shown to be bogus that young-earth creationist organizations have warned against making such claims, clearly young-earth creationism is not 100% true. And if the “if it’s not white, it’s black” logic of young-earth creationists is right, then young-earth creationism is false.
Also, as the relatively recent invention of Seventh Day Adventists, from where it spread to be adopted by large numbers of Protestant and smaller numbers of other Christians, this viewpoint cannot possibly be exempt from the utter falsehood that is the state of all human claims and ideas.
Unless, of course, young earth creationists are wrong about everything being either completely true or completely false…but that would require them to consider evidence, discuss issues of interpretation, and deal with nuance in a manner that the worldview of most YECs does not allow.