Very low-tech, but seems to work reliably enough for the purposes. And if it's not right , then that pretty much means the person's computer clock is off.
Which the person may not have any control over.
Well no, but if they're staring at that incorrect clock, then I think it's acceptable to present them with an incorrect time that is at least in sync with their incorrect time.
That presumes that they've noticed the computer has an incorrect time.
Possible scenario: they have a bus or train or whatever to catch. They spend a bit of time on TP and notice the chat is being used for the group they're interested in. The computer is wrong, say behind by 20 minutes. They don't notice the difference, but do see the time on chat and realise it's about right. They chat and base the time they need to quit by the time on chat, and due to that miss the bus or train.
It might be a bit far-fetched, but possible?