And a stopped clock is right twice a day. So all the stopped clock merchant has to do is wait for the clock to line up, then shout from the rooftops that they have the right time.
It's not enough to be correct by coincidence, process matters. We see this often enough in scientific papers where the statistics come into question. News process is different, especially given how sources work. Not everyone is willing to be recorded, and recordings are increasingly untrustworthy anyway, so at some point you have to start believing that the reporter heard person X say Y.
The worst part of the whole fake news fiasco has been people using the (very real) problems of the established media as an excuse to switch to consuming total nonsense from fabricated sources.
Interestingly, time itself is a social construct. Not just in the sense of relativistic time, but in the sense of how we came to move from individual local clocks ("decentralised time") to using time from the communication network which had to coordinate internally ("railway time").