Interesting story. I'm from the same area as Run Kid Run. The band is actually a band called Side Walk Slam with the addition of a fourth member. Neil a member of the original Run Kid Run joined Side Walk Slam after their original guitarists departed. They then switched their name to the name of Neil's old band Run kid Run after one album.
I have a 4 track Run Kid Run demo that has Neil on vocals and features an entirely different line-up of the band. It in my opinion is the best Run Kid Run thing I have ever heard. The official albums just sounds like Side Walk Slam to me.
To answer your question simply haha...they are a band on Tooth And Nail Records.