Slight correction:

The last company's letter would be:

    [Company]: We have decided to move forward with another candidate. Thank you for your time and good luck on your search!

And I agree, these HN threads always shock me to no end. I keep finding apparently you can negotiate when you are in the demonstrably weaker position. I still haven't heard those magical incantations and I, like you, keep asking but nobody is telling.

Apparently they are secret.