Thank you everyone who read this blog entry. I discovered a way to import YouTube captions into Arc and wrote another entry about it: YouTube Captions to Arc (updated 26 Oct. 2018).
It is awesome that YouTube videos can be played inside the Arc media player and thereby allowing instructors to use all of Arc's goodness with videos from that source. In my U.S. history classes I'm going to have to work in some late-90s popular culture so I can use Arc to make pop-up videos of VH1's Pop Up Videos.
Unfortunately, the Arc media player does not recognize that a YouTube video has been captioned. It is possible to show the YouTube captions within the Arc media player by opening the video within a YouTube window and enabling captions there. Hopefully Instructure's developers will be able to figure how to have Arc Recognize Captioned YouTube Videos. Until then, our students will get an opportunity to practice their fine mousing skills in order to make those captions appear within the Arc media player. The embedded video demonstrates the following workaround: