What lies are you specifically talking about?
A lot of people have the impression that China is some sort of black hole: no information gets out, so who knows what's going on inside?
There is a huge amount of information coming out of China. People I talk to there tell me about what their everyday lives are like. There are millions of Chinese people communicating with the outside world every day. What's certain is that the situation is completely different from how it was in late January through February. The epidemic really does appear to be under control there.
> Contact tracing is a nice to have, but not important. The important things are healthcare capacity (aka ventilators) and population monitoring.
What you're proposing is a control strategy, in which the epidemic is held at a level that doesn't overwhelm hospitals, but in which a large number of people continue to be infected each day. It's a steady state with R ~ 1 and a manageable case load. In the US, this is the current situation, and it means a steady pace of ~2000 deaths/day.
In that strategy, the second you reduce social distancing measures, the epidemic will flare up again, because you're balancing on a knife's edge.
The strategy that China pursued was suppression (R << 1), followed by containment of the epidemic at a much lower level. In the first phase, extreme social distancing and quarantine measures reduced the number of new infections to a small number (tens/day). In the second phase, social distancing measures have been relaxed, and widespread testing and contact tracing are being used to try to catch nearly every new case in the country. That's only feasible if the number of cases is small.
This two-phase strategy is the only one I can see that does not lead to ~0.5% of the population being sacrificed.