I'd probably redo it too, though I'm weird that way. I think most people would consider it a "design feature" and move on. (If you can make the other sock match, it will strengthen your argument that it's a design element.)
One downside of frogging socks is that since the yarn is fairly fine, it often gets kinky -- if you decide to go that way, you'll want to straighten it out before starting to knit again or your tension may turn out really wonky. (I think grumperina had a pic of this phenonmenon on her site.) All you need to do is make a small hank (I make one out of the kinky part when it's still connected to the rest of the skein), wet it, smooth it out, and let it dry. If the kinks are stubborn, hang a small weight on the bottom of the hank while it's drying.
There is no right way to knit; there is no wrong way to knit. So if anybody kindly tells you that what you are doing is "wrong," don't take umbrage; they mean well. Smile submissively, and listen, keeping your disagreement on an entirely mental level. They may be right, in this particular case, and even if not, they may drop off pieces of information which will come in very handy if you file them away carefully in your brain for future reference.