> There are Wikipedia pages which are flat out wrong (by any common definition of the term) and yet the editors won't allow any corrections because the primary sources are also wrong.

Primary sources aren't really considered reliable on wikipedia (with some exceptions), so if such a situation is happening (and you have a source for whatever version you think is correct, since just trust me bro doesn't go far on wikipedia) and you can't resolve it on the talk page, probably time to escalate the situation.