My impression was that they made advanced predictions what a gravitational wave observation would look like from a binary black hole merger, and then they measu

My impression was that they made advanced predictions what a gravitational wave observation would look like from a binary black hole merger, and then they measured pretty much exactly that. This is why we believe the machine worked. The other reason we believe them is that they (together with VIRGO) found a neutron star merger, and that was confirmed by many other observations in many different spectra.