Something similar we do at work is write a quick document on why something isn't possible.

A bug can't be reproduced? Take a video of it working fine, and show the logical path for how the bug couldn't happen.

Can't build X in 3 months? What's the minimum for X? What's the missing component that takes 2 months? We can't have a partnership with A, but why wouldn't it be possible to have a partnership with A's competitor?