"Fair use" covers specific uses like education, commentary, or parody. You can't choose to 'release it under fair use'. Sampling someone's work, modifying it and using it in your own music is not necessarily fair use, and the burden of proof falls on the defendant.
You’re absolutely right that the burden of proof falls on the defendant.
Fair use is judged in courts based on four factors: the purpose and character of the defendant’s work, particularly whether it is commercial or not; the “nature” of the copyrighted work; the amount of the copyrighted work used in the defendant’s work; the effect of the defendant’s work on the market value of the copyrighted work.
There are multiple defenses I can think of that pertain to multiple unique uses of programs like Audacity involving copyrighted work. There’s a whole section of the Internet dedicated to mashups of songs, some of them obviously parodical in nature (leaving for an open-and-shut case), some of them obviously meant to be more like something you’d put in your music library. Could prosecution argue that such diminishes the value of both (or more) songs? Absolutely, though the defense could just as easily argue that one who has these in their library is most likely a paying listener of these songs, either through purchase or streaming—leading to virtually no loss in the value of the copyrighted work.
The legal system has always been a mess as far as sampling goes, I’ll just say it. I would argue that the use of samples in a free piece of otherwise-original work even less so diminishes the market value of the original work. Someone might hear a sample and say “oh, what is this?”, go on WhoSampled, find the original track, and start listening to it through either streaming or purchase. This has happened to me countless times.
I’m not a lawyer, and I am quite certain that any defense team could come up with even more substantive arguments than this, particularly given their knowledge of the ins-and-outs of the written law.
Now for a very, very subjective opinion: the literal only thing record labels are interested in with cases like this is money for themselves. Not for the artists, songwriters, producers, mixing engineers, etc.—it’s for the chief executives of the labels. Given such, it leaves a bad taste in my mouth to have their legal teams going after the same kinds of creatives whom they f— over even while being signed to their label.
The new Audacity keeping track of users’ IP addresses is, as I said before, shameful. Along with whatever other data they’re collecting with the previously mentioned incredibly vague statement about being in compliance with law enforcement.