It's pretty telling to see Germany refusing to buy F-35 or Hungary buying ones in order to piss off Sweden.
And if you're going to be training pilots... Shouldn't you do it on the exact config of F-35 that Denmark's buying? Which means a Danish F-35, which means leaving it in the US.
Having a military costs money. Living up to treaty obligations like NATO costs money. Trying to have a military on the cheap just ends up with dead troops/pilots/sailors.
India also has lots of land.
That aside, it's more or less common knowledge these days that the planes have not been delivered for all these years due to the production problems they are still having.
Esquire just did a piece just month mentioning that the plane starts to fall apart if it's flown too fast and the computer fails to detect if the plane is flying to fast about half the time.
This aircraft program still has a ways to go.
We don't know what the "training in the US" requirement looks like, though. I wouldn't be surprised if it was just "you need to use Danish planes to train" + "we only have training facilities in the US, and if you want to bring your own that'll cost money". It has nothing to do with "Denmark can't make its own decisions", because as far as I'm aware that hasn't been alleged anywhere.