Nope, this is Apple thinking it's smarter than you are and that you really want your phone to be two steps ahead of you. I've been trying to disable this functionality for years and I suspect that support people are told this functionality doesn't exist or else they are told it does but also taught how to pretend it doesn't exist. There is apparently a bunch of things you can enable and subsequently disable, like 13 different setting changes, that will ultimately prevent this but it also disables a ton of other functionality.
Yeah, these are features not bugs, because there are enough people out there that will be "shock and awe'd" by this that they have no reason to disable it. It's like the app drawer, none of the instructions I have found to make them so I that I'm not constantly hitting the emoji button in my text line. They all say they do, but they don't. And it's not my handset, I've had 3 different 5S models that all do it, my 5 didn't and none of the others before it did.
Specifically, what worked for me as their option 3"
---- Option 3: Disable Cellular Usage of Music App to Stop Autoplay
If the music app that is auto-playing is streaming over a cellular connection, you can disable that apps ability to use cellular data to prevent it from streaming any music and thus disable auto-play of music from that app.
Go to the “Settings” app and then to “Cellular” and scroll down until you find the app(s) in question that are auto-playing music in the car from your iPhone. Turn the switch to the “OFF” position to stop them from using cellular data.
So far (two calls) it's solved the problem.