This is definitely a Galaxy S3 bug. This has happened every time I run with my phone. At first I thought it was my armband, but I took the phone out and held it in my hand, and the phone kept doing the same thing. However, pressing on either the volume up or down button would sometimes fix it, but then it would continue to do it again. This obviously made me think something was stuck in the buttons and the moisture/condensation while working out made it conduct and short the buttons. However, I just realized this ONLY happens with headphones plugged in.
It might be just headphones with a microphone as those are the only ones I've used.
When I switched to bluetooth headphones, this has stopped happening.
It's definitely a bug with the phone.