The "warning" wording isn't an interpretation, it's how diet member Kazuya Kondo framed the event before a government official agreed
From the April 17 Diet transcript:
近藤(和)委員:「先般、日本の政府から米国に対して申入れをした、部課長級ということですよね。確認です。」
政府参考人:「はい。そのようなことでございます。」
Natural translation you can double-check:
Kondo: “The Japanese government recently made a representation to the U.S., and this was at the director level, correct? Just to confirm.”
Government official: “Yes, that is correct.”
The key part here is the term mōshiiree (申入れ). It doesn't have a single-word English translation but means to formally petition|object|submit a complaint/warning/concern. In diplomatic context, the closest English equivalent is "representation." From Oxford:
representation [singular] formal statement made to somebody in authority, especially in order to make your opinions known or to protest
But if the title said "Japan Makes Official Representation to US" people would be rightly asking wtf am I talking about, who's repping what? 😅 It's simply not a word that's in the common vernacular, and GR news are meant to be maximally accessible, not require you to open a dictionary to understand what's being said.
You're 100% correct Japan can't really do anything here but the article doesn't suggest otherwise. All they can do is issue strongly worded warnings, complaints, protests, objections, which is what they are saying they've done repeatedly. Any potential infringement complaitnts would be on private copyright holders to pursue. But it's clear the Japanese companies so far preferred lobbying with Tokyo to try using its soft power to make this stop instead of suing the U.S. government in... I think the Washington DC federal claims court would have the jurisdiction here?