“If you don’t complete your work by the date given by your instructor, the lapsed failing grade becomes permanent. The instructor will assign the new grade to replace the Incomplete.”
While I am sure the OP is long gone the school’s verbiage is very specific and prohibitive. There is a passive element such that if you don’t complete the work within a communicated time period the F becomes permanent. The proactive element is that at that point the professor has to “assign” the new grade.
The OP states the professor and others have lied.
If the OP was claiming I was unable to complete the work in the prescribed timeline due to illness perhaps there is a compassionate Dean that would listen. However saying the professor approved my withdrawal but never gave me a timeline for completion and then just assigned me an F and I was unaware of the rules that are readily accessible is hardly a path to victory in my opinion.