You are thoughtful to be concerned, because this IS reason for concern. Girls of 11 are sensitive about things like how they look and smell and she likely will be devastated if a classmate, or someone at summer camp etc., says to her, "You smell like pee."
The doctor found no physical cause but did....nothing else at all? No recommendation to the parent to deal with "holding in pee and poo"? Sounds like a doctor who is not very proactive. The mom should pursue having another doctor check into whether the girl has physical issues with holding in urine and poop; and then the mom also needs to have open communications with the girl about other, non-physical reasons -- Is it possible that the girl has always tended to "hold it" too long since a younger age? Or that she might have wet herself more seriously once in front of others and now just holds and holds until she leaks, out of fear of urinating at all? Have there been any changes in the girl's life at ALL -- divorce or parental strife, a new job for mom or dad that has changed the family schedule, a new sibling or a sibling who has needs that demand mom and dad's attention, issues at school, issues with friends? The mom might rack her brains and say "There's nothing to stress her," but you'd be amazed at how kids can internalize stresses that an adult would just not even see as a reason for stress.
If this started about a year ago, what changed then? Was there some possible trigger like starting a new school, getting more pressure about homework, again--a new sibling or change at home, anything?
If this were my daughter, and I have one just a bit older than this girl, I would first see a different doctor; then I'd think hard about her history with toileting and whether this is a possible case of weak bladder/uretha from years of holding pee; and for sure I would investigate whether there is something psychological and emotional going on that I as the adult didn't recognize. I hope your friend does not hesitate to investigate all that and get the girl help including counseling if needed.
Meanwhile, if the girl can admit to the fact she does "leak" at times -- it would be good if mom can get her to wear mini-pads (or maxi if needed) and change them regularly to reduce the smell.