I don't know what Churchill thought of us, but I'm sure it wasn't flattering. He probably thought we were backwards opium-smoking yellow monkeys
. But that wouldn't be an uncharitable impression, given the state China was in at the time. The verity of a statement is totally independent of whether one likes it or not. Anyway, we set out to prove that late-19th/early 20th century China was a totally anomalous period in our history, and we accomplished that. Have you proved yet that Churchill statements on India were only applicable to India at the time, and not intrinsic to India as a civilization?
Anyway, you seem to be confused about Churchill's (or anybody else's) understanding of the term "country". Cultural and religious similarities, or a "unified identity" does not make a country. Only political sovereignty does. When were the instances of unified political control? The British Raj would be one instance. Mughals were also close. Two foreign dynasties that did not use Indian institutions but imposed their own (rendering your "unified identity" argument invalid). But I can't think of any other instances.