The petition seems to be saying SoundCloud should permit mashups and bootlegs. Perhaps I do not understand the current use of those terms.
It appears that if a DJ samples pieces of another artist's recording, then recombines them in new and interesting ways to produce a new recording that the original artist never intended, that is a mashup. It is also clearly a derivative work of the original artist(s) phonorecord. Even very short phrases of actual recordings have been found to infringe the copyright of the original.
It is somewhat more difficult to find a creditable definition for bootleg, which always implies an illegal activity. Surely the petitioner cannot intend that complete distribution of copyrighted recordings should be made available. That is the kind of file "sharing" that has brought down dozens of websites and peer to peer systems. More likely he is referring to unauthorized recordings of artist performances, which has been common since the invention of magnetic tape, and which is also pretty well established as illegal. Or he might be thinking of an unlicensed "cover" of a songwriter's work, which is clearly infringement.
The petition seems to be requesting that SoundCloud adopt a policy that would permit if not encourage copyright infringement, making it potentially liable for damages. If, as stated, the petition intends that SoundCloud should serve as a way for people to have access to the original works of otherwise voiceless musicians, it is hard to see how turning it into the target of the anti-piracy minions, armed with established copyright law, will serve that purpose.