That article seems to state the opposite?
Most of what we know about pre-republican Rome is from oral tradition, not actual records. So if by the time of the Republic February was the second month of the year, it was the second month of the year through all of recorded Roman history.
I really don't doubt the authenticity of the story, I mainly was trying to indicate that we don't know when the change occurred but it certainly happened a long time before Caesar: by his day, the change was an oral tradition whose full story was lost in the very distant past.
Not just "for most". It has negative connotations (of the kind reffered to here) for all people.
"Legend" connotes "didn't take place".