I mean, there are scenes in the movie that call for the military being there regardless of SHIELD.
It really just seems like a line to me.
Out of all the movies they listed where they did help, with the exception of Iron Man which was largely ambiguous, the films in question portrayed the military as a paragon of heroism and moral fortitude.
In this movie, you have a government agency of some kind (SHIELD) building WMDs in secret based on presumably illegal Nazi weapons designs, and government officials, one of whom (the one who does all the talking and represents the group) is American, ordering a city of seven million people to be nuked.
That seems to be the more likely reason why they pulled out, the fact that the film made fairly passive criticisms of the government and military. The US military has a pretty shady history of caring about their image as an inherently noble institution more than putting in the effort to actually be one, so this seems pretty par for the course.