And even if you are forced to set unreasonable terms, you can still come away not looking like complete jerks.
You don't end up with a PR firestorm pounding the team that was being reasonable if both are truly negotiating in good faith.
If you're negotiating in good faith, you protect the interests of both parties. You stay neutral in your conversations with other people not privy to the conversations. You say things such as, "BYU and UW have been in talks but have yet to reach an agreement."
What you saw coming out of UW is dirty and unprofessional.