The problem isn't in her assumptions. The problem is that she (materialists) can provide no coherent explanation for truth or "the adequation of thought and reality."
"Truth is the recognition of reality; reason, man's only means of knowledge, is his only standard of truth." -- Ayn Rand
Truth is the product of recognition(i.e., indentification)of the facts of reality. Man identifies and integrates the facts of reality by means of concepts. He retains concepts in his mind by means of definitions. He organizes concepts into propositions -- and the truth or falsehood of his propositions rests, not only on their relation to the facts he asserts, but also on the truth of falsehood of his designations of essential characteristics." -- Ayn Rand
"The truth or falsehood of all of man's conclusions, inferences, thought and knowledge rests on the truth or falsehood of his definitions." -- Ayn Rand
Regarding Ayn Rand, you wrote ... The problem is that she (materialists) can provide no coherent explanation for truth
With regard to religious "truth," Ayn Rand has a great deal to say about mysticism. Here is a short beginning, an excerpt from her essay "Faith and Force: The Destroyers of the Modern World."
Mysticism What is mysticism? Mysticism is the acceptance of allegations without evidence or proof, either apart from or against the evidence of one's senses and one's reason. Mysticism is the claim to some non-sensory, non-rational, non-definable, non-identifiable means of knowledge, such as "instinct," intuition," "revelation," or any form of "just knowing."
Reason is the perception of reality, and rests on a single axiom: the Law of Identity.
Mysticism is the claim to the perception of some other reality -- other than the one in which we live -- whose definition is only that it is not natural, it is supernatural, and is to be perceived by some form of unnatural or supernatural means.