I'll try to clarify my reasoning.
From a purely legal perspective, the US is not bound by domestic Danish law under any circumstances (and vice versa: cf the doctrine of state immunity).
From the perspective of legal philosophy, the US cannot break Danish law in Greenland, because Danish law is not legitimate law in Greenland, any more than Israeli law is legitimate law in the West Bank. You'll certainly find other perspectives on this within legal philosophy, but any philosophical argument that attempts to reconcile the premise that (a) colonialism is illegitimate, and that (b) colonised or occupied people are nonetheless bound to obey the legal order instituted by an occupier is necessarily going to be quite contorted.
From the perspective of Western liberal-democratic political philosophy, government without the consent of the governed is illegitimate, its laws lack authority, and it is the right (and duty) of the people so governed to overthrow and disestablish that government, which they have no obligation to do peacefully or within the bounds of the existing political order (e.g. many wars of independence, American Revolution, etc).
Ergo, the US cannot violate domestic Danish law in Greenland, both because that's legally speaking nonsense (state immunity), and because domestic Danish law is not simply not legitimate in Greenland. Were Denmark not occupying Greenland at the time, the US government would be able to negotiate with Greenland about the possibility of placing a base there, and the Greenlanders themselves could decide whether this is something they want and what benefit they are able to secure from such a deal (Iceland, for example, has greatly benefited from such an arrangement, being able to secure its freedom from Danish colonialism with US assistance). Denmark's domestic laws, and the extent to which Denmark does or does not enforce its laws, is a domestic matter for Denmark. In as far as it purports to legislate for other countries, and then not even obey those laws itself, that's - again - a domestic matter for Denmark.
I hope this clarifies my argument.