For the Danes to trust spies requires willful naïveté, no? I wouldn't be surprised to hear key Danish politicians got bribed or blackmailed into being so credulous in the first place.

They are neither bribed or blackmailed, every danish government for the past 20 years have been informed about this agreement and has complied. It's absolutely a crime against the population (since innocent Danes are also being spied on). The reason the politicians are complying is that we are reliant on US for military support through Nato (which I guess you can call a bribe, of sorts)

Diplomacy and military alliances are complicated. When you catch another country breaking their promises you make a fuss (sometimes public, sometimes not), doesn't necessarily have anything to do with whether you were are aware of the possibility before.

Willful naïveté can be a strategic move as well