That's still not proof of any such conversation happening.
Denmark joined because the US invoked Article 5 after 9/11. It was more about making sure they're protected if they ever need it in the future, so I'd say it was absolutely in their interest. This was the first time Article 5 was invoked, not going would've killed NATO and their own security. The invasion of Ukraine has solidified their reasoning.
No, of course they wouldn’t make such pressure official. But it’s not exactly a secret that the U.S. arms industry has a lot of political pull. Not hard to imagine that such pull extends to “helping” NATO subjects to pick the right suppliers.
As for article 5, that might explain the second gulf war and/or Afghanistan, but certainly not the first gulf war, Libya or Syria.
Whenever Uncle Sam says “jump”, you’ll see all the small NATO states lining up to ask “How high?”.
Denmark joined because the US invoked Article 5 after 9/11. It was more about making sure they're protected if they ever need it in the future, so I'd say it was absolutely in their interest. This was the first time Article 5 was invoked, not going would've killed NATO and their own security. The invasion of Ukraine has solidified their reasoning.