Directly quoting Starship Troopers completely by accident because you are yourself a caricature of a fascist is a real America as hell kind of thing to do
It seems more likely that it was a freak accident that they blamed on the bugs.
Also, crack pilots who can plot optimal interstellar travel routes seem to completely buy it. Carmen has high math and science scores and pilots ships with FTL capabilities. In order to fling a meteor from Klandathu to Earth, the meteor would have to be propelled using FTL technology. But Carmen's evidence for the superiority of the human race includes that they developed interstellar travel, so it seems that they don't believe bugs are capable of it. It's a point of controversy that bugs even possess rudimentary intelligent.
So it implies that either the federation and the military are far stupider than they appear to be (plausible given their constant incompetence and poor education system), or they are so receptive to propaganda that they ignore the most basic logic (also plausible).
Not surprising given how bad they are at their jobs. Carmen, a top pilot, is unable to dodge an asteroid with plenty of warning time. Two dropships crash into each other in the Klendathu drop.
When Ace gets his hand skewered with the knife, it's played as a cool badass lesson for rookies. But he actually was asking a great question, and their training is terrible at preparing them for combat against their actual enemy.
Ultimately, the fascist society loves war for its own sake. They love abusing each other and the aesthetics of war and the concept of eternal combat. As such, victory becomes tangential or even undesirable.