That's not really true though, is it? Spanish flu started in either France or the US, bird flu probably started somewhere in Asia, swine flu was first found in Mexico.
At the time the Spanish flu was thought to have originated in Spain, so it was designated as such. I know after the fact there's been a lot of speculation that it was started either here or France. If that was the conventional wisdom at the time, it'd be called Etaples flu, even if that doesn't roll off the tongue quite as well.
Ebola virus-first found by the Ebola River.
Lyme's disease is called Lyme's disease because it originated in Old Lyme Connecticut (and I actually can't tell you how much my mind was blown that it wasn't officially diagnosed as its own condition until 1975. We put man on the moon before we found out about Lyme's disease?!?!).
Honestly, I do not think he'd be pressing this as hard as he is if the Chinese weren't continually trying to absolve themselves of the blame. It's a direct freak you to Xi Jinping.