Further to my earlier reply - a more succinct way to look at it might be:

- When they fix the run time, bug A goes away. So the proof still holds and the zlib code is still correct.

- When they add a system of proofs for the parser and modify that, then bug B goes away. So the proof still holds and the zlib code is still correct; and now more of the library is proven correct.

The formulation of the title is "I was told X but that's not true"... but that's not true. You were told X, and X is true, but you found Y and Z which are also important.

What is the program?

There are two different answers to this question, and which one is "correct" depends entirely on the context of who is asking it.

1. It's the code that is specific to this program that sits above the run-time layer (internal view, that most programmers would take).

2. It's the code in the binary that is executed (external view, that most users would take).

The key question does not seem to be "was the proof correct", rather "did the proof cover everything in the program". The answer depends on whether you are looking at it from the perspective of a programmer, or a user. Given the overly strong framing that the article is responding to - highlighting the difference in this way does seem to be useful. The title is correct from the perspective that most users would take.