I was told this during my judicial committee (some five years ago) when I brought up concerns I had with the "truth." In addition one of the elders (who was an engineer) said once you've accepted a proof of Pythagorus' theorem you don't later start doubting that theorem. I thought that argument was a weak analogy then. However, I now find this argument ironic after reading this:
How do we know that such and such “theorem” are true, if the proofs are almost certainly full of errors?
Well, we don’t. In mathematics, as in large parts of natural science, it is an unfair fight. We can “easily” show a purported proof is false by finding an error, but we can never know for sure that it is correct. (Even if you apply a formal proof checking technique, you can never know for sure there was not an error in that process.)
What happens in practice is that once several experts in the domain have examined the argument and declared themselves to be satisfied it is correct, then the rest of the mathematical community accepts that fact and moves on. The more people look at it, the more confident we get.
However, there have been times when this process was eventually found to have gone wrong. Arguments that have been accepted for some time are subsequently found to have a fatal flaw. That’s why mathematicians are reluctant to ever say something is totally correct.