EDIT: I should note that these could be harmless <a...> links, but most aren't, and I'm too lazy to update the regexes and rerun. You get the point though.
Quite the opposite. The video -- because it's huge compared to JS, CSS, etc. -- /does/ make sense to host on YouTube. The /player/ does not belong embedded in the page though. Take a screenshot, host that on your own crummy web server, and link to YouTube, ideally with a notice to the effect of "Clicking this link will share your information with YouTube..."
EDIT: I should note that these could be harmless <a...> links, but most aren't, and I'm too lazy to update the regexes and rerun. You get the point though.