I answered not 100% sure but would lean toward games are "influenced".
I kind of thought after the Patriots won in 2001... the league wanted them to win that year because it was right after 9/11. The name "Patriots" and their colors were red, white ,and blue.
I think the league is "pulling" for the Bills this year. As neutral to the Bills/Bengals game I really dont see why it's not played in Cleveland? A city right between the two teams. Also, why didnt the refs measure the last third down conversion the Bills got yesterday? Granted I tended to think Buffalo got the short end of the stick a lot of times but this year they are getting some nice treatment.
And yeah with all this Fan Duel, draft Kings, billion dollar deals the NFL has wit the companies.... its human nature things would get influenced so to speak