Not true.
First, you need to get your music out of the iTunes prison on your Mac. Your music needs to be individual AAC (or whatever) files that you can copy & move around just like any other file.
Move your music files to a folder you created on your Mac.
Next you need an app that can connect wirelessly to your Mac from your iPhone via wifi.
FileBrowser works for this.
Once the music files are copied over to FileBrowser on your iPhone, you can play the music files within that app or send them to another app that can play them (Goodreader etc).
You won't get any artwork or graphics associated with your music, just the music and file name, but you'll be free of the Apple Music & iTunes prison.
I don't know what happens with DRM protected music that was purchased from the iTunes Music store. It probably won't play this way.