One of the reasons that Trump wanted to break up NATO was specifically related to Germany's reliance on Russian gas: https://www.reuters.com/article/us-nato-summit-pipeline/trum...
Trouble is, the summit took place in July 2018 and Tillerson was fired by Trump in March. (From Tillerson's Wikipedia article: "... Trump allegedly suggested a tenfold increase in the U.S. nuclear arsenal, which would cost trillions and take centuries. These reports were denied by White House officials and by Trump after which individuals familiar with the meeting told journalists that Tillerson either called Trump a "moron" or a "fucking moron.")
It's not clear why Pompeo would have pushed this particular agenda item, only that Trump likely didn't come up with it on his own.