My DD is also 4 and having accidents. She has been to the pediatrician and is fine. I've spoken to her teachers. The teacher assures me that DD is not the first nor the last child to need to be reminded about going to the bathroom. I would do things like no longer allow her to sleep on the couch or only sleep on the couch if she's in a pull up or underjams. If she pees on the rug, get Nature's Miracle to clean it up. I told my DD that if she wants to do things like go to a neighbor's house for a playdate or she wants to go to a birthday party, she must use the potty. I remind her all day long as if we were earlier in the potty training process. I praise her when she is dry, and make her clean up when she is wet. I tell her she must stop what she is doing and go right away. One of my DD's problems is she'll realize she needs to potty, and then get distracted on the way to the bathroom. I'm working on her to just GO to the POTTY and not pet the cat, etc.
So I'm with the doctors. I think it's behavioral. Your daughter and mine are not the only kids who have had this issue. It is frustrating, but not unheard of.