This is exactly right. The pace at which someone stops walking and starts jogging/running can vary greatly per individual (as was already stated). During the full marathon last year, I was running and was passed at mile 6 by a race walker doing faster than a 10:00 min pace. No way could I walk that fast--heck, apparently, I wasn't even running that fast.
13 minute mile could be anything. We have pretty long legs, but we have "jogged" at that rate. Yes, we would likely have been faster walking at that point, though. It all depends. For some, 13 might be a decent pace for a jog.