I think they are implying that public domain works are attacked globally because a company thinks they own it in one country. Take Happy Birthday, for example: in the UK it is considered a traditional song and is therefore public domain, but in the US there are no such protections against copyright and therefore Time Warner thinks they own it.
The problem is that Universal is the owner of the copyrights (including the lyrical and syncronisation copyrights), and this is DMCA we're talking about. This would end up differently in Europe or UK (the original authors are irrevocably entitled to some percentage of the revenue, typically 5%) but DMCA is based on American laws (which do not have these protections).
Maybe even in a commercial context. In fact it's quite likely that concerts get treated specially. The issue is, these automated censorship tools don't encode the nuanced clauses of such contracts. They err on the side of banning, even if it's perfectly legitimate.
Also IMO in the digital age it's so stupid that teachers can't even read a book to children via Zoom without a license...