One thing to bear in mind is that headlines are not prose, they are shorthand.
So you have to assume there could be missing words, since that’s how headlines work.
In this case there is a dropped “just”:
Don’t (just) validate: parse!
If the headline was “Parse, never validate” then I would agree with your reading. But “don’t” is pretty lightweight. I’m having a hard time thinking of a lighter discouragement word. Given that, I think it’s unfair to assume the strongest discouragement is implied.
The title of the post says "don't validate," and so I initially expected it to relate to the mantra of being liberal in what you accept, etc.