No, the answer is almost certainly something else. Blame robots.
YouTube has a system called "Content ID," which allows the owners of copyright on material to automatically censor unlicensed use of said material. As described here, YouTube automatically matches videos against a big database of copyrighted material, including music, when the video is submitted. Then, copyright owners can, if they wish, block a video from being viewed.
During his announcement on Tuesday, Rand Paul entered and left to the song, "Shuttin' Detroit Down," as Business Insider notes. The song is a twangy lament about the state of the economy that dates back a few years; the copyright stamp on the YouTube video reads "(c) 2009 WMG." WMG, of course, is Warner Music Group.
We've reached out to both WMG and YouTube for comment, and will update this article when we hear back. But it's hard not to see some humor in the situation. Rand Paul's spirited cry against government intervention has been blocked from view because YouTube lets huge music companies preemptively apply copyright law.
Looks like Paul just got another plank in his campaign platform.
Update: A YouTube spokesperson responded without shedding much additional light: "YouTube’s Content ID technology gives rightsholders control of their content on YouTube. If a user believes their video was claimed in error, they can dispute the Content ID claim." We have not yet heard back from WMG.