It is entirely possible for the iPhone to use the battery faster then it can charge. If you are streaming data, are in a weak signal area, have the screen brightness up, location services and wifi on, then you could easily use more juice then any charger can handle.
Remember that the charging circuit is designed for maximum battery life, not maximum charge speed. I don't believe the iPhone is smart enough to just use the power input instead of the battery, and again, I don't the current is that high.
Try turning the brightness all the way down, and turn off location and wifi if you are not using them and then stream your music and see if it makes a difference. If you are in a weak signal area that will contribute to faster battery usage.