I implore you to at least google what "stable" in the US means, and find whatever cherrypicked source doesn't include "conscious". It's probably not going to be one from the US, or one that cites its sources from the US.
In the mean time, the wikipedia article contains the summary.
https://en.wikipedia.org/wiki/Medical_state
"The American Hospital Association has advised doctors not to use the word "stable" either as a condition or in conjunction with another condition, especially one that is critical, because a critical condition inherently implies unpredictability and the instability of vital signs."
Stable cannot be used as a blanket status (in the US). You can even sue the hospital for even issuing a "stable" blanket status, but probably not the news for issuing a falsified statement cause "muh 1st amendment".