>that "its" does not work that way.

Can you expand on what the mistake is?

It's missing the antecedent. So for this to make sense in Eng it should read:

Taiwan, in contrast, revamped its [own|healthcare|something] top to bottom.

Otherwise it looks like "Taiwan, in contrast, revamped its [top] [to [the] bottom]."

>It's missing the antecedent. So for this to make sense in Eng it should read:

It's not missing the antecedent, it's near the end of the previous sentence, just like the other person you replied to said.

Singapore, which we wrote about in October, tinkers with its health care system all the time. Taiwan, in contrast, revamped its top to bottom.

The its clearly refers to health care system from the previous sentence.

True enough. It's just not common usage to use "its" as an absolute possessive like that. Whereas other possessives lend themselves to that usage.

In other words it's typically used as a possessive determiner in this construction.

It's somewhat similar to the following:

-Have you eaten?

-Yes, I've.

And thus your first statement gets completely overshadowed by a minor, and to me meaningless, grammatical discussion.