The movie studio could now hold HN liable.
Well, except that HN is not under EU jurisdiction, so it could probably choose to ignore EU court decisions against it. Bigger platforms of course won't have that luxury, so they'd need to come up with some way of limiting or avoiding that liability... or maybe just blocking EU users.
He's using the quote to make an unrelated point. This wouldn't be considered copyright infringement anywhere you have an impartial judiciary.