This isn't just a theoretical claim. People read Euclid's Elements for over two thousand years before noticing a missing axiom. That's the sort of basic mistake that any properly-working machine proof verification system would immediately reveal. Published math proofs are often later revealed to be wrong. The increasing sophistication of math means it's getting harder and harder for humans to properly verify every step. Machines are still not as good at creating proofs, but they're unequalled at checking them.
There are "competing" systems to Lean, so I wouldn't say that Lean is the "one true way". I like Metamath, for example. But the "competition" between these systems needs to be in quotes, because each has different trade-offs, and many people like or use or commit to multiples of them. All of them can verify theorems to a rigor that is impractical for humans.