"I get the same where I work - something won't work, we tell the big cheeses it won't work then they have trouble believing it didn't."
BTDT. Kept the correspondence. Produced it when they tried to drop the resulting clusterfuck in my lap.
It's amazing how fast "We can't possibly spend XYZ to make your impossible demands happen!" change to "How much do you need to make this work?" (to which the answer is invariably "three to five times as much as it would have cost if you'd given me the correct budget in the first place and it will take weeks to fix, not tomorrow, longer if you don't fuck off from breathing over my shoulder 24*7")