https://en.wikipedia.org/wiki/Treaty_of_the_Danish_West_Indi...
[1]https://www.execfunctions.org/p/the-danish-west-indies-prece...
International courts almost always reject these arguments because they want treaties to be stable, but when a state (like the US or the USSR/Russia) has the power to back up their argument, they can be successful
It's clear that the threat of Denmark falling into the hands/influence of another power, not the fall itself, was enough. In case it wasn't clear, Lansing writes "the possible consequence of absorption," not, "the absorption of Denmark."
The US position was that Denmark was too small and weak to remain neutral or defend the islands. Therefore, as long as the islands remained Danish, they were a security risk to the US.