Using "rather" to correct a misstatement

Solution 1:

That's fairly acceptable usage.

As with so many words in the language, rather can be used to mean several different things.

• somewhat/moderately,
  e.g. "In height he was rather over six feet, and so excessively lean that he seemed to be considerably taller" - A Study in Scarlet
• considerably/considerably (yup, kindof the opposite of the previous meaning),
  e.g. "“I flatter myself that I have managed it rather neatly,” the detective answered proudly" - A Study in Scarlet
• preferably/instead,
  e.g. "If my view of the case is correct, and I have every reason to believe that it is, this man would rather risk anything than lose the ring." - A Study in Scarlet
  e.g. "Having finished his scrutiny, he proceeded slowly down the path, or rather down the fringe of grass which flanked the path, keeping his eyes riveted upon the ground." - A Study in Scarlet
  e.g. "‘Arthur would rather that we spoke the truth,’ the girl answered firmly." - A Study in Scarlet

It's in the third sense that your sentence employs rather. I've used several examples for this particular meaning to demonstrate usage.

Of course, the way you use it is more common in speech than in writing. What you are doing is squeezing out the "or" from the sentence and flipping the sequence.

That is why I have chosen my own particular profession,—or rather created it, for I am the only one in the world. - The Sign of the Four