Our use of YouTube videos is not only allowed, but also actively encouraged by the YouTube API monetization guidelines, which can be found here:
https://developers.google.com/youtube/creating_monetizable_applications
The following is an excerpt:
“Remember, the best way to make money using the YouTube APIs is to use your imagination. To be more specific, you should use your imagination to think of a new way to let people interact with videos and then build an actual (not imaginary) application that enables such interactions to take place. And, to be even more specific, your application should provide a service that people are willing to pay for or that presents advertising opportunities. However, those advertising opportunities should not violate the YouTube API Terms of Service (“API Terms of Service”) available at http://code.google.com/apis/youtube/terms.html as described in the following section. We can’t wait to see what you build!”
Our video player and instant, interactive captions is a great example of such “a new way to let people interact with videos.” Also, we don’t interfere in any way with the ability of YouTube and its content partners to monetize off of advertising revenue on our site.
We should also note that we use content uploaded by official YouTube partners who are the actual content owners. When uploading videos, such content owners have expressly allowed for their videos to be embedded on other sites such as our own so that they can monetize through ad revenue.