Could it be that the Grumman designers had already read the RAE test pilot's reports on the FW190 when they put together the Bearcat proposal, and the Grumman pilots flight in the FW190 a couple of months later were just a confirmation of what they, or their bosses, had already read?
The RAE FW190 was captured on the night of 16/17 April, so there was plently of time for it to be test flown and reports circulated to Grumman by the time of the 28 July memo.