Well, it depends on what your definition of a "formal agreement" is. If you mean a signed contract, then the answer is - no - many people work without a signed contract. Remember, Tubby Smith worked for several months here without a formal signed deal. Billy Gillispie never signed his formal deal with Kentucky, if I recall correctly. I believe they each had a "memorandum of understanding" or a "letter of intent." I suppose that's what Williams should have gotten in this case, too, but I'm guessing tons of assistant coaches move around based on verbal agreements, etc. Remember, it is an absolute rat-race at that time of year with assistant coaching hires. Speed is very important. If Williams thought he had an offer from Tubby, he was doing his previous employer - Okie State - a favor by letting them know swiftly so they could find a replacement at a time when good assistants are in high demand.
Remember, if a guy with the character of Tubby Smith offers you a job, you probably figure you have the job. Tubby apparently had the carpet pulled out from under him by the administration, which I think based on the circumstances - was reasonable. Tubby thought he had autonomy to hire, but as it turned out it, he didn't - based on whom he was hoping to hire.
It really sounds like an unfortunate situation, but I agree with Sour - I think Williams is entitled to some compensation.