That math, though technically accurate, doesn't allow for the effect of increased testing. I'm confident that cases are increasing in CA, also confident that they aren't doubling every 4 days. "Confirmed" (or maybe "presumptive"- not yet confirmed by CDC) cases may be doubling every 4 days, but I don't know how much of that doubling is due to more testing and how much is due to actual spread of the virus. I suspect the increasing test rate is responsible for much of the increased numbers.
Hard to know how accurate the Chinese numbers are as their media belongs to the government. However, that's less the case in S. Korea, and they've apparently blunted the epidemic more than other nations.
While testing is still very important at this time as a surveillance tool for decision making, the time for it to have a dramatic impact on doubling rate is unfortunately gone for a lot of areas in the US.
It is only effective for that purpose at the beginning when there are very few cases and small levels of community spread and you have the man power to track, isolate and heavily contact trace every case to delay the initial wave and buy you more time to avoid a total lockdown.
Once you get to a certain level of community spread, you have to just lock down those areas like Wuhan and the northern Italy region did to contain the virus. Unfortunately most of the covid 19 affected areas in the US are past that point already.
If you look at my Forbes link for exponential growth, a doubling time of 4 days is actually pretty good control. Many countries with much more aggressive testing than the US have current doubling times at 3 days at the moment. That is how infectious this virus is.