I wouldn't laugh and shrug this off so easily. Fair Use has been interpreted many ways.
One such way is to say that only the companies that own the copyrights (note: COPY rights) to the music hold the right to make a copy of it. Under that definition, purchasing the CD does not give you the right to copy it (which would include creating an MP3) because you may have purchased the music CD but you still don't own the rights to the music itself, so as much as you may laugh, a legitimate case could easily be made with the right judge (and no, I'm not talking about payoffs).
This has been a claim within many forums of media for years, but most seem to err on the side of "Loss possible money loss, no foul." The warning at the start of every movie does not say "copying is illegal UNLESS you purchase the movie and then it is ok". Creation (not necessarily distribution) of video game ROMs has been declared illegal for many years by companies like Nintendo who state that Fair Use copying is limited only to themselves a single backup copy in case the original gets damaged. Professional photographs cannot be reproduced by anyone except the original photographer until 70 years (or however long the length is) have passed. The fact that you bought the photo does not allow you to go just anywhere and get it reproduced. You are supposed to only go back to whoever owns the rights to the photo... which isn't you. (I have been turned down several times by professionals on asking old photos be reproduced for that reason.) And lastly, of course, it is illegal to record your favorite sport from the television without expressed permission from several people.
Naturally, none of these will likely result in the FBI busting down your door. My point is that other media outlets have been making these same claims for far longer, and apparently they have not been shot down outright by the courts as ridiculous claims. I see this falling right in line with those.