No. For one thing, the LIGO experiment is not finished; observations are nowhere near complete. But even if it did fail, all that this would have established would have been that this particular experiment was not able to detect gravitational waves. There are several reasonable conclusions that could be drawn from that:
* Gravitational waves do not exist.
* Gravitational waves do exist, but their properties are not the same as we expected and hence this experiment failed. There is a very big difference between "the model is not exactly the same as we thought" and "the model is outright wrong".
* Gravitational waves exist, but there was a flaw in the experiment that prevented it from detecting them. Either the experiment was poorly designed, not sensitive enough, or equipment failure stopped it from working.
Which of these conclusions is correct depends on the circumstances, and analysis of the results would be necessary to determine which is the case. In all likelihood, new experiments would be needed to confirm either way and obtain more data. It is very rare that a single experiment is the be-all-and-end-all of a given issue. Drawing conclusions as a result of a single experiment, and abandoning all further investigation, is bad practice, and often further investigation can shed more light on the incident.
To use your court analogy, what you are proposing is like interviewing a single witness, and if that witness hasn't seen anything, assuming that nothing happened and not bothering to interview any other witnesses.