I have just been amazed at all the unique remedies for fixing this. Before reading this, I would have taken out my ripper and just got going. Now, I have options when I run into this small seam problem. I always keep some kind of lightweight iron on, sew friendly, interfacing on hand and now have a new use for it. Thanks once again to these super quilters who share info so freely and make quilting more fun for us all!
Because I would want to know it wouldn't fray out, I would probably iron on the lightweight stabilizer, then stitch the seam again with a much smaller stitch to make sure everything stays in place.
The key will be to buy a lightweight interfacing/stabilizer than only has one side that irons on. And, secondly, only get it on the seam that needs repairing, so you will need one of those pressing cloths that doesn't allow glue to stick to it, or maybe a piece of wax paper to keep the interfacing from getting where it doesn't need to be.
Good luck with your repair.