I hope you understand the context in which that was said. The point of that statement is that the only way to rigorously verify correctness of a program is by using formal methods. Those are often too difficult to achieve by humans, which is why there is an entire program of developing autoformalization using LLMs. You are supporting what I have said.

In practice, no one rigorously "proves" that their program works at present, and well-written tests do suffice. The definition of "well-written" here is circular, granted, but there isn't really an alternative. Even strong programmers should be writing high-quality testing suites.