If the stated TR counts of the PLA AESA is accurate, it means the Chinese have not just caught up but surpassed the US in this AESA technology and all within one generation. It is also not inconceivable that there is a technology limitation with the miniaturisation technology with both the US and Europeans that they have ended up where they are today. Implicit in your statement is that the Chinese have breached the technology wall that has until now limited the US and European. Given such significant strides in technology advancemen, it is not unreasonable to expect some evidence beisdes inconceivability.
Well, we have to remember that some of these Chinese fighter AESAs may have started development later than some of the US and western AESAs, that is to say they are able to leverage more modern technology even by a few years, which may account for the difference.
In other words, if the US were to develop a new fighter AESA starting today, it would likely have much higher TR module density than the J-20's AESA (assuming equal radar size).
Or a practical real world example.: APG-80 equipped F-16E/Fs were first delivered in 2003. This radar has a TR count of 1000. Over a decade later, J-10B starts deliveries in 2014, with a similar sized radar but with a slightly higher claimed TR count of 1200. Given the decade gap between deliveries and likely similar gap in start of development, is the difference in TR count really that contentious, considering the past experience Chinese industries have had in developing and mass producing AESAs prior to this? Recall that 052C and KJ-2000 with AESAs were delivered in mid 2000s, so development would have begun years before that, with research even further back. So it is definitely conceivable for them to have gathered experience from previous endeavours to reach parity, and when combined with developing a new radar for J-10B (or J-20, J-16 etc) they would have the benefit of using more modern and recent advances for their TR modules as well.
So while I can understand the skepticism and I do think it is worth discussing, in this case I think there is a plausible explanation for it.