There is a large difference between putting up a few percent of their constellation to reach initial minimum viability and putting up enough satellites to properly cover the rest of the world (a very expensive endeavor that will take years).
Plus, the US Government may directly benefit in a very big way from utilizing Starlink and that may make it a bargain compared to the alternatives. If US defense contractors were building that constellation, they'd be spending ten times what SpaceX is.
And that's before we get to the potential for intelligence gathering globally. The powers that be will be all over that, no matter what SpaceX claims to the contrary (SpaceX will have a gun to their head and will not have a choice, just as the Prism gang had no choice).