Copyright law prohibits those who have copy of something from making and distributing unauthorized copies. But if you receive one of these copies, I don't see what law that would break or why the receiver would be responsible.
Interesting position, Most of the lawsuits however have sued over DOWNLOADING and uploading, not just uploading or "distributing" infact in some cases it has been shown the copyright owners themselves were distributing the content to catch people "illegally downloading" the content.
That would also mean downloading from Usenet would be completely legal...
However, yes, my understanding of copyright law is that it only limits those who currently own a copy from making and distributing more. The relevant US Law is actually very short, take a look at Section 106: https://www.copyright.gov/title17/92chap1.html#106
(Edit: 106 lists what it is against the law to do, as you can see from 501 which talks about punishment etc. https://www.copyright.gov/title17/92chap5.html )
I'd like to know more about these lawsuits.
I don't think that's your responsibility. If it is brought to your attention that the app is infringing copyright, maybe it's your responsibility to stop using it.
But it's not your responsibility to verify that every service you use has the rights to all the content it uses. How could you possibly do that?