To continue to what archerno1 said, there is no way you know for a fact your friend cheated. Unless you were with them 24/7. With that said, you also have to remember when they do ban waves for 3rd party programs they also put them with people who buy/sell accounts, people who account share, as well as boosted players. Those are all against the rules, and from what i remember all get permaban since those are serious offenses. It could be that she had given her account info to someone, or someone stole her account and in turn used hacked. But your friend would need to contact support and tell them a date to when her account was compromised. But as i said they take stuff like this seriously and because of that need information that she should only know. But that all lies in if her account was compromised. If she willing gave her account to someone else, then she has no one else to blame than herself. It stated in the ToS/Summoners Code not to give your account information to anyone, there really isnt a reason to do so anyway.
Now i know absolutely nothing about how Riot detects hacking and the likes. But im pretty sure they have some of knowing. They have been in this business for a number of years, and while hacking and the likes will always be a problem, they have kept it pretty low with their time in this game (i can honestly say ive never need a hacker/scipter in this game) With that said, its obvious that there is something on her computer and Riot's detection caught something. They dont go around banning people for no reason. The detection caught something, whether she used it or not is irrelevant. the fact is that its on her computer. This is the reason why Riot doesnt like 3rd party programs at all and while some are in the gray area (skins/voice) the fact remains that they cannot control what these developers are doing with the programs. it could be getting personal information, could be giving your players viruses. they dont want to risk that chance.
All im saying is if she didnt do anything wrong, Im sorry but i just cannot believe that you are 100% sure she didnt download anything to her computer that "might" have caused the detection to see its running while the game is loaded. its impossible unless you are with this person 24/7. If she really didnt do anything wrong she (not you) should contact support, give as much information she can if she is actually telling the truth. If you are going to waste their time please dont bother. There are people who need actual help and people who are breaking the rules trying to cheat the system has no place here for that!