Adafruit trinket power question
You are thinking of the power pin in a digital manner.  The power pin is not set to be an input or an output.  It is just the positive terminal of the power rail.  If you want to power the trinket using a 5V power source, you'll put it in there since its the positive terminal.  If you want to power another device that uses 5V and it just so happens that the 5V rail connects to the trinket as well, the device will still be powered.  

The trinket isn't sourcing the power, the battery is, or in this case the power supply that the battery is connected to.

The LEDs aren't pulling their current from the trinket but rather the power supply.  All the trinket is doing is sending the signal through the DIN pin.