I have nothing invested in whether or not any given mathematician is right or wrong. I just picked a random example of a controversial proof -- the point was more that proof-as-computation could settle and any all disputes.
It might not lend more understanding to people not invested in "field X" (or even people who are invested in field X!), but it would be proof.
Proof in the current world of math is quite intangible.
I think the demand for "tangible" proof (if by that you mean, fully mechanically-verifiable proofs and a style unlike anything common in mathematics papers today) is a bit silly and seems to be driven by some ideologies well outside of mathematics, rather than mathematicians themselves.
A proof is whatever convinces sufficient mathematicians that the theorem is consequent! Classical logical systems are a very good way to do that so they get used a lot. But they're not the only way, and involving a computer program makes most proofs less convincing rather than more.
It might not lend more understanding to people not invested in "field X" (or even people who are invested in field X!), but it would be proof.
Proof in the current world of math is quite intangible.