If I recall details of this story as it was breaking - there was an emphasis that the US tried repeatedly to communicate with counterparts in China to discern the nature of the balloon and cool the situation. From memory, the Chinese side refused to engage on any level... which ultimately led to the balloon being shot down.

The Chinese are advanced - there's no chance they couldn't/didn't monitor a balloon of this size launching into their airspace. There's no chance they do not know the true origin and owner of the balloon.

If it were civilian/private and/or university - this would have been easy to explain and prove. The balloon may have still ultimately been downed (it was violating airspace regardless of who owns it) - but the situation would have gone rather differently.