In this situation, do I have any obligation to tell the Board they are being misled? Am I allowed to tell the Board?
CEO is misleading the Board, I am an officer, private company
If you have a Chairman of the Board, discuss it with him first or discuss it with your lawyer (since you are an officer, you will share the blame when ugly things hit the fan). Get your evidence ready even if you are not planning to do anything about it now.
Document, document, document.
Test your views/findings with a trusted confidant. Is it simply commercial/financial or is there an brand/ethical/legal risk to the company?
Refine your views/findings then approach the board member who best will listen objectively. Maybe take your personal attorney to that meeting...
Be aware you may need to negotiate an exit package.