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>Is the case against the authenticity of these sightings circumstantial or did investigators go there and look and not see her?

There aren't details
of the investigation.
Three commissions, though.

Father Vlasic was suspended last year by the Vatican's Congregation for the Doctrine of the Faith amid an inquiry into his conduct after three commissions failed to find evidence to support the visionaries' claims.

The shrine's kind of lame,
however the article
says the town does well:

This represents a massive blow to millions of Medjugorje followers worldwide who were hoping that the Vatican would one day legitimise the controversial shrine.

The seers have grown wealthy as a result of their claims – and so has their town, which has boomed as a result of the ‘Madonna gold rush’.

Some today own smart executive houses with immaculate gardens, double garages and security gates, and one has a tennis court.

They also own expensive cars and have married, one of them, Ivan Dragicevic, to an American former beauty queen.

Is the case against the authenticity of these sightings circumstantial or did investigators go there and look and not see her?

It is a 'case' that is not provable or disprovable at this point. It is not likely that someone will go to Medjugorje, investigator or otherwise, and "see her". There have been many investigations and videos over the years of the visionaries during actual visions where they have been poked, psychologically analyzed and monitored (Scientific Research on Medjugorje visionaries). For information on what the Popes are reported to have said, [and clearly the Pope cannot individually say anything “official” regarding this matter at this time, it must be done in accordance with the process of the Magisterium - anyone remember this about the Passion of the Christ movie? (It Is As It Was)], about Medjugorje, here are some links:

Pope John Paul II

Pope Benedict XVI

IMHO, if Pope Benedict XVI felt that Medjugorje was not authentic, he would have acted to stop it by now.