I agree that the numbers may not be accurate. These numbers came from thermal imagery. Fly a satellite over a Chinese nuclear power plant and record its heat signature. This will allow you to calculate the thermal output of the powerplant and thus the Pu production. However, there are ways to cheat the system (for example, additional cooling structures or reactors hidden from satellites) so the numbers are not necessarily accurate.
However, even if we discard that possibility and focus on the lower numbers themselves, it is hard to believe that China only has 200 warheads. China can produce well over 1000 weapons even with cold war era technology, which is why silos are being constructed now. I think it is more than a shell game. China actually needs more delivery vehicles and the silo project is partially mitigating the problem.
Feeder reactors only and then also only known reactors. China is a
BIG place with lots of underground facilities and secret bases. It's also fairly easy to shield your known civilian feeder reactors to prevent those signatures to be obtained to perform any decently accurate estimate on production rates. The estimates regardless make it obvious that China's absolute bare minimum is still probably enough for 1000 warheads of high yield assuminig Yu Min configuration is similarly efficient/wasteful of material use.
Exactly not only is it hard to believe China has 200 or 300 warheads, it is logically bewildering once the reasons for those estimates are listed. Those being literally, China has paraded x number of ICBMs and if we assume 3 to 5 warheads per type of MIRV capable missile then we reach this number, and China hinted to us so in since and really only in the 1980/90s during a time when China had every reason to underplay it and still sort of do for public image but western elites probably get the memo of general range of real numbers.
China doesn't want to publicly announce to the UN it has x. For deterrence, it allows the US intelligence to collect enough info and show them enough to let their leaders know the real number is well above 1000. This allows China to not be condemned in a western led public shaming parade like they always do about how "China is a scary and dangerous threat" and also achieves deterrence because the people who should know, do know.