No, it wasn't clogged with a soda bottle or a glove. There was a "strainer" installed in the downspout near the top of the pipe, with six small holes the size of a pencil eraser cut in it. It rained and small debris from the roof immediately filled the little holes, hence the clog and the overflow.
We had to have the whole thing cut out.
I'd call that a poor choice in strainers considering the amount of water the boxgutter is designed to move, but at least now (crossing fingers) we can keep the rain off of the house, not in the second floor, not in the basement and away from the house and into the storm drains.
We'll see. It's supposed to rain for the next three days.