You hit the nail on the head.
> In China some people must have been amazed how the US was arranging such a thorough cover-up all by themselves.
Exactly. Even in India we were amazed by the cover-up. I am pretty sure every Asian country knew it was a cover-up. The very first reports on Coronavirus I came across was not even in the media. It was on a Korean Youtuber who posted regular video updates on the virus leak in China even before the news was picked up in the West. He was warning how CCP was arresting scientists who put out information about the virus and even sharing videos of doctors who had recorded themselves warning about the virus itself (one of the first few who treated patients of the virus and fell sick themselves). I can't, for the life of me, find that channel on Youtube anymore. But yeah there was, and still is, a lot of censorship aided and abetted by Big Tech.
The death of the doctor was widely reported on throughout the pandemic[0][1][2].
[0] https://www.theguardian.com/world/2020/feb/06/whistleblower-...
[1] https://www.telegraph.co.uk/global-health/science-and-diseas...
I think this is for a few reasons; America is a [the?] global hegemon; so American domestic politics have some earnest global relevance. But more than that; reporting one country's news is more efficient than reporting N countries' news. Fewer stories means fewer writers to pay, less research and investigation to do, etc. Furthermore people have an appetite for news, but a finite appetite; sate people with news about America and you'll have them thinking less about local issues. Therefore, news organizations in other countries have both an economic and political incentive to report American news instead of local news. What's more, America encourages this because for America it is a form of soft power to live rent-free in the minds of everybody else.
Point is: when a narrative becomes taboo in American media, that's likely to rub off on the rest of the world. Particularly so in countries where a sizeable portion of the population consume at least some English-language media, participate on English-language forums, etc.
In China some people must have been amazed how the US was arranging such a thorough cover-up all by themselves.