grammatical number - Pronouns for collective nouns (British and American)

British and American English differ in the way they conjugate verbs for collective nouns: http://languagelog.ldc.upenn.edu/nll/?p=877. For example, an American would probably say "China is winning" whereas a Brit would probably say "China are good."

Similarly, I think the American would say "The Chinese gymnastics team is good" and the Brit would say "The Chinese gymnastics team are good."

My question: what happens when pronouns enter into it?

Brits can say "The Chinese gymnastics team know that they are good." I think that's straightforward enough.

But what about the American equivalent? My American coworker argues for "The Chinese gymnastics team knows that they are good."

To me, this seems to create a clash between the plural "they" and two earlier cues that the subject of the sentence is singular: (1) "team" and (2) "knows." Even if "team" can work as both a plural or a singular, can it really do both in the same sentence?

My personal inclination is to write it as "The Chinese gymnastics team knows that it is good." I suggested this one to my coworker, who didn't like it. I agree that it's weird. Having three consecutive singular cue-words gives too strong a sense of the team's collective conscience, which wasn't implied at all in the British version.

Maybe this question is particular to the verb "know" and isn't (as I originally thought) generally applicable to sentences with both collective nouns and pronouns. But in any case, I'd love to get some opinions on how an American should fill in "The Chinese gymnastics team knows that [???] good."

(I've lived in Britain for 9 years, and America for 12)