The bulk of your rebuttal is exactly my own point. Peer review doesn't actually prove anything one way or the other. The ultimate truthfulness of a cited proof is all that matters. The idea that cited proofs should be peer reviewed don't add intrinsic validity, it just fosters academic laziness.
"Boy that's a fantastical claim that doesn't seem right; but all the citations are peer reviewed and I see nothing obviously wrong so I guess its true!" -OR- "Boy That's a fantastical claim that doesn't seem right; I don't see anything obviously wrong here so lets double check the cited proofs they based this on."
What's the practical upside to only using peer-reviewed proofs besides speed at the cost of fidelity? What's the practical downside to using unreviewed proofs besides "more work"?