> the best outcome for them is that they AND EVERYONE ELSE go high
But it's really not. The best outcome for them is that they are 100% accurate.
Now, I understand that that's generally not feasible, but assuming that you need to pad everything by a huge amount is part of the problem.
As a general rule, I've found that the kind of answer that gets the best response is on the order of "about X time to complete development, Y to get through testing, Z if you need any documentation, release notes or user instructions, I think A, B & C are risk items that could delay completion. If Sally and Jared aren't around for us to ask questions, that will also delay things so we need timely responses from them."
Give good answers and you'll find people take you a lot more seriously.