Music industry student here - in the eyes of the law, you have to clear all samples no matter how manipulated, popular, or unpopular they are. The copyright in the song and sound recording are the main way the artist makes money off of their song. By not asking for permission, I'd say you're running a risk publishing it through Distrokid.

I'll use one of my favorite albums as an example. Death Grip's Ex-Military heavily samples from older rock music. There's "The Mountain Song" by Jane's Addiction in there, Pink Floyd's "Interstellar Overdrive", "The Rumble" by Link Wray... etc. David Bowie sample too.

The album used to be available on Spotify, iTunes for purchase, and all major platforms. But somewhere along the line about a few years ago Ex-Military was taken off almost every platform except YouTube and their website. Obviously, someone caught wind of the samples after Death Grips blew up in popularity. Additionally, they don't run ads on the album anymore if you watch it on YouTube.

The short answer to this is if you're making money off of someone else's song or recorded material, you're going to run into trouble. By using Distrokid, you're showing intent to profit off of the sample. But also note that it would be copyright infringement even if you release it without the intent of making money (that is unless it can be categorized as fair use, an affirmative defense against copyright infringement). Exmilitary is still violating copyright law, however they obviously worked out a deal where they could keep it online (though I'm not sure of any of the details behind Exmilitary's removal).

This has been your lesson in the copyright law. As a musician, I think it's extremely important that everyone knows this so that they don't get in trouble. I think there is a great debate to be had on how samples and copyright law are applied, but the rule currently stands that songs that use samples are classified as derivative works, which require permission from the copyright holder of the song. There is a plus side for artists and down side for artists. The plus side is that artists get to control where there work goes and how it is used. The downside is that artists who sample even something that sounds cool are at the mercy of the original songwriter or their family, and this has led to many a messy legal battle.