Their music is their property and it is protected by copyright (because that is the law against stealing for this kind of property).
You don't understand copyright at all. Let an attorney educate you:
First, bottom line - no one is taking anything from these musicians. They never had any such right in the first place. They're claiming that any song inspired by theirs that sounds kinda similar is infringement. It's not and never has been. Regardless of whether a person or a machine does it.
Copyright is a time-limited (if ~150 years can be called that) set of economic rights (Euros say moral rights too, but that's stupid). Copyright is not "it's my work, I have absolute control of it". Uses outside those economic rights are not governed by copyright. News reporting, educational use, libraries - copyright cannot be used to prevent these things, they are explicitly allowed. Fair use (US) / fair dealing (UK) gives conditions where use does not infringe on copyrights, notably considering how much of the work is used and whether it's done for profit and whether the use is transformational or verbatim. Example: news reporting on a copyrighted work is explicitly allowed, even when news is for profit and verbatim, as long as a limtied excerpt is used that's less than the entire work. That's simplified and with slight inaccuracies, but close enough for a non-legal audience.
The trouble with the artists' argument is that they're essentially complaining about learning. "That there AI learned mah werk and made more kinda like it. That ain't fair!". Except humans do the same thing all the time; that's how creation works. If you have a blackbox that takes existing music in one end and outputs similar music on the other end, that box could be filled with a person or with an AI. The artists are saying "It's infringement when the black box contains AI but not when it contains a person". Perhaps that's their policy wish, but that's not what the law says.
Nothing happens in a vaccuum ex nihilo. Every artist combines influences from previous works when making anything new.
There's even a legal test for this: derivative work. If a new work copies too much from an existing work, then it's termed a derivative work and triggers copyright protection on the original work. Derivative works are deemed to borrow too much.
The flip side is, you can borrow a lot from previous works (every work does) and as long as you don't cross that derivative work line, then you're ok. Your work is considered new enough that it doesn't infringe on previous works. Doesn't matter whether it was made by a person or an AI. That's not part of the legal test.
The main factor is: are these new AI-generated songs too similar to prior songs that they constitute a derivative work? From the AI songs that I've seen, any sane person would almost surely say no. They do sound similar and take inspiration from the original, but do not cross the line. Except the music industry is so screwed up that they consider even a 5-second samples of a beat or riff to be infringement. Like when a hip hop song makes a totally new song with new music and new lyrics that incorporates a few seconds of a heavily modified version of a well-known riff from another song - music industry says that's infringement. See Supreme Court case Acuff v Campbell Rose where 2 Live Crew sampled a few beats from Pretty Woman - not infringement. Compare to any other creative industry - movies, literature, painting, etc - and music industry's views are asinine. No one outside the music industry takes musicians' views on copyright seriously.
