I lived through a pretty thorough lockdown in Shanghai. Much stricter than anything in the US.
Every alleyway community and apartment building had a guard sitting outside at a table making sure only residents entered. Outsiders would have to have a resident come down and escort them in -- after showing ID, registering their name and phone number and getting a temp check. Those guards, mostly volunteers, sat outside all night during some crappy February and early March weather.
Masks were obligatory since late January (roughly Jan 23), with near 100% compliance. And people continue to wear masks in public, though the mask rate dropped to about 60% - 70% in June. The reopening was handled gradually and carefully. My one gov't gym is still closed, not set to reopen until September. Universities not set to open until the Fall term.
After the bad start when the virus was first being identified, and the resulting large Wuhan/Hubei outbreak, China has been a model on how to contain the virus. Not too different than what the US CDC has advocated with regard to reopening the economy and schools except that the Trump Admin just discards those policies in favor of high risk stupidity.
China masked up early and thoroughly. That was a key. Really China hasn't gone in much for social distancing and handwashing. My two complaints: the airport allowed flight disembarkees to all bunch up in a mob at two points, instead of either single file or spacing (or both) & I had hoped that soap would become more universal in restaurants and other public bathrooms (some have soap, some don't).
So yeah, I believe what I've lived through. There were a few weeks in Feb when 3 friends messaged me about an alleged case at the hospital directly across the street from me, and another purportedly at the nearby subway station. But from the precautions I've seen and talking to people including my friends at a major hospital, I'm pretty confident Shanghai had a minimal number of cases. City of 20M.
I trust that the SH gov't wouldn't allow bars to be open and crowded if there was still transmission. Their reputations and careers are on the line, but they also just want to do the right thing and protect everybody's health and safety. Imagine that? Too bad that kind of thinking didn't infect Trump and GOP governors.