It is true that "The safest course is always to get permission from the copyright owner before using copyrighted material." I think it would be a great exercise for someone here to actually do that and report on the process. (I do 99% original material, so don't look at me just yet.)
Rules or not, I likely wouldn't post a cover on a music-promotion site such as Karamoon or any other. But I wouldn't worry a lot about posting it on, say, box.net for auditioning by listeners here. I'm pretty sure that,
in practice,
Fair Use covers it. Cp. notes 1 and 4.
Just my unqualified, nonlegal opinion.
R.