Let's take for example the song Viva la Pompeii, a mashup of Pompeii by Bastille and Viva La Vida by Coldplay, both copyrighted songs. As far as I can tell, the mashup itself is not copyrighted.
If I want to use a mashup song like this one (contains copyrighted music, mashup itself is not copyrighted), is it legal to use a Youtube audio downloader site or similar to obtain an MP3 file of it? My guess is no as it contains copyrighted music the video author doesn't (appear to) have rights to redistribute.
If that's the case, would it be different if I have purchased all the songs included? So in the above example, if I have purchased a legal copy of both Pompeii and Viva la Vida, does this change things?
Please note: I don't intend to monetize or redistribute in any way, I'm only concerned if it's legal for personal use. I'm specifically concerned with US law, though I would be interested to know if it's different in other countries.