if the PC can stream it locally, then it has enough horsepower, right?
Not necessarily. When you play it locally on your PC using something like VLC Player, then you are not transcoding because you have the necessary codecs on your PC.
On the other hand, when you play it via Plex on a remote device, depending on the format of the actual video, that video may need to be transcoded before it's sent up to the remote device. Transcoding process is resource intensive.