Cameron Dubs
Making David Cameron Sing!
Their musical artist are allowed to cover the songs, yes, but that's something completely different. That doesn't mean they can just use the original in any way, shape or form. Yes, he probably has the rights, but not through that deal.
According to many sources (e.g. Billboard.com, Hollywood reporter, etc.) the deal covers the monetization of original soundtracks throughout their entire musical library, which also allows covers to be monetized.
Do a quick google (looking for billboard.com in particular) and have a read. See what your opinion is on the article.