They CAN also sue for patent infringement, intentional infliction of emotional distress, loss of consortium, hurt feelings and a whole bunch of other things. That doesn't mean they have any legal basis to do so.

Copyrights are not at all involved here -- this is about trademarks and related doctrines, such as dilution. As I mentioned above, the one circuit court decision I could find on the subject held that the trademark laws do not apply to claims against the federal government.