I think that this is actually more common than people realize. Not only do kids get easily distracted at this age and wait a little too long, the sphincter muscles work differently in kids of different ages. If it only happens at home, it probably isn't a medical issue, but I would still have it checked out. At home things you can try is Miralax (it is possible that she is constipated - sounds crazy, but it's true) for a few days (it is over the counter now). If it seems like she may have a mild bug, you can put her on the BRAT diet for 48 hrs to see if that doesn't clear it up. Finally, I would ask her not to flush the toilet after she poops for a few days - check and make sure that she is wiping appropriately and also how her stools look in general so if you do take her in you can answer questions about that (the dr will ask). You could also consider putting her on a bathroom schedule for now.
As far as making her pay - I wouldn't. You would feel terrible if it ended up being something that wasn't her fault. As far as making her clean it up - as long as you aren't doing that as a punishment, it is fine - certainly people who make messes, even if it is an accident, can clean it up :)
Good luck and remember - this too shall pass :)