Task killers like this are not needed, and are counter-productive, on Android.
Android is not Windows, it's Linux. It manages memory completely differently (and much smarter) than Windows. It attempts to keep recently or frequently used apps in RAM so the next time you use it the OS doesn't have to reload it from storage. If an app needs more RAM (or you start an app that's not running), Android will automatically kill a background app in order to make that memory available.
"Free" RAM doesn't get you anything. Running apps won't use more RAM than they need, so having unused RAM doesn't make your foreground app run faster. ALL RAM, whether used or not, has to be constantly refreshed, so having unused RAM doesn't save you battery. Finally, most apps aren't really "running" when they're in the background. They're inactive, just waiting to be called on. There are exceptions, like email, Facebook, and others that do stay active, but the way to manage that is to adjust their sync intervals. Except Facebook, which is a true battery hog, and which I won't have on my phone. But if you use it, look into the greenify app, which will keep it from restarting all the time.
When you kill apps yourself to create more "free memory", Android sees that available RAM and puts it to use, often by reloading the app you just killed. That wastes cpu and battery.
So to answer your question, Battery Doctor isn't exactly bogus. It does kill the apps. It just doesn't do anything to keep them from coming back. Apps like this were somewhat useful back in the days of Android 2.x, but not any more. The one app in this class that can be useful is Greenify, which will prevent the OS from automatically restarting apps you "greenify." But even that is counter-productive for apps that you use fairly often. It uses less battery to leave them in the background than to kill them and restart them later.