Both depend on whether you believe in the government actually. When we say "Chinese state media", we're really talking about a media controlled by the government, especially for those political topics
This would be true even with private actors, at the end of the day it's whoever has concrete evidence of something taking place.
If the FBI is going to make the broad statement that China is hacking the USA, it'll have to back that statement up by evidence presented in court against individuals the FBI has investigated for hacking into US companies/government orgs.
Seems that you just don't believe the other side has done some investigation and therefore did not search for it. I'm not saying that either incident is fake but you've just proved my point of view.
You are correct that we choose what to believe based on what we think is more likely or useful. We don't have time to research all the things
But that is not relevant to point that Chinese state media (which is in a way all their media, like becoming in Russia now) is wrong and lies regularly but will never undermine the cult of personality at the top of the government that owns it by admitting the lies.
To deny that you need to go all tinfoil on me and say most instances where they lied is made up by the West. Like idk Tiananmen didn't happen or whatever. If you believe that then sure.