I think that the best way to repair a faux pas like this would be to go ahead and bind the edges as you would for the one on the correct side, then blind stitch the hole closed. Making a fabric-to-fabric repair will never be invisible, so go ahead and make it obvious, but with a "finished" appearance. No one will ever know that it's not there on purpose, and you could make up some great story about it being "reversible" or some such.