There is no reality. Life is about perception. Somehow in some ways, their perceptions of you define who they are. Their perceptions are their truth. Not yours. Your ability is limited to managing perception, not to control their interpretation. Their interpretation is theirs. Not yours. If it works on your advantage, the discussion sounds like a win-win. If it does not, it is no longer your mistake.
Update on Dean Kowalski: Runner-up