If aliens showed up on Earth it would be FAR more likely to be observed and photographed by multiple civilians than the military. Civilian eyeballs outnumber the military by a couple orders of magnitude. You'd probably see it on Instagram first.
Milwaukee, 2018: https://www.youtube.com/watch?v=0mkRgPGncn0
If I were studying a primitive species, I would be no more interested in their war fighting than any other aspect of their society. Maybe that is just me.
If they are concerned about our militaries more than other things, why would they not always be perfectly concealed?