I do not know.

On a conservative news site called Liberty Sentinel. 

Maybe it is, maybe it isn't - but who cares? The source documents are posted there for anyone (who reads Spanish) to see for themselves.

As of the present time (24 October 2020), the definitive answer to that is 'no' - but the possibility that the courts documents might be a clever forgery is not a valid reason for the UN not to bother investigating the allegation....

All that someone has to do is check with the Chilean authorities; and that is something the UN Secretary-General should be able to do in 10 minutes with one phone call. 

Who knows?  That is a question for a Chilean judge..... but the question doesn't matter:  regardless of whether or not this case succeeds in court , the underlying facts do not simply evaporate into the ether....

If, as is alleged, the High Commissioner has lied about having a medical degree, the Chilean court case might still be dismissed for any one of a number of reasons - but that will not change the fact that she has done something for which lesser staff members are routinely "separated from service".

That is a question for the Secretary-General.

The UN has spent millions (maybe billions) of dollars promoting the 'Rule of Law' to corrupt nations - but what happens when the Organization is faced with this sort of dilemma?  Does the Rule of Law go out of the window because there is one rule for senior staff and another one for everyone else?

If this is all a big mistake and the information from Chile is wrong - fair enough, let us drop the matter and move on.  It would then be up to the HIgh Commissioner to counter-sue for defamation, if she feels she has been falsely accused.

But in order to get to the point of being able to prove the allegation is false, the Secretary-General first has to  investigate the allegation - because, from the UN's perspective, this looks like a prima facie case of misconduct 

Investigating the allegation should not be too difficult; the plaintiff in Chile has done all the work already - it should just be a case of verifying his information to prove that he is wrong.....

Probably not.

After all, the prospect of actually holding senior staff accountable under the UN Staff Regulations and Rules without fear or favour and regardless of their position would set a seriously dangerous precedent!

Genuine accountability could a cause the UN universe to unravel, leaving the Secretary-General with so many vacancies for USG's and other senior staff that he might have to advertise for more on jobs.com.......  

The odds of that happening only slightly less than the odds of Jimmy Hoffa being found alive, living with Elvis and a domesticated sasquatch in an apartment above a pizza shop in Jersey City.....

Why would he push Michelle Bachelet under the bus when he clearly failed to act on Kate Gilmore?

Kate Gilmore was the UN Deputy High Commissioner for Human Rights.  Michelle Bachelet was her boss.  

Gilmore claimed to have post-graduate degrees in Social Work from the University of Melbourne and in Community Development from the Royal Melbourne Institute of Technology.

In May 2018 however, two UN whistleblowers reported that this was not the case. They had contacted the universities in question and confirmed that she had never obtained any such qualifications as she claimed.  

Oh dear.

So what did the Organization do?

Nothing.

Six months later, Kate Gilmore was allowed to leave the UN without a stain on her record….