I think the word 'false' may be problematic here, as it implies a dichotomy of true/false. Putting on my anthropologist hat for a minute (OK, it is hard for me to take it off), all religions and religious philosophies have a few things in common:
-the core teachings or philosophies
-a hermeneutic component, that has to do with how texts (including oral presentations) are interpreted
-a subtextual component related to a shared culture among practitioners.

Teasing these apart is difficult. The Christian denomination in which I was raised, for example, includes a directive to "love your neighbor," explicit rejections of homosexuals, and a overwhelming popular support of the idea of American exceptionalism. At different times and in different contexts, each of these may be part of the core, an interpretation of the texts of the religion, and/or a cultural common ground among members that is not directly referenced in the religion proper. So, to say that the teachings are 'true' or 'false' belies the complexity of reality in-the-moment.

We each perceive the world, and our chosen path, through a veil of ego; we also communicate our understandings through a veil of ego. My current understanding is that, though that veil has no substance, it is also complicated by all our social and material ties.

-Untei