A physicist friend of mine said, half jokingly, that with that much money poured into the project they had no other option but to find that damn boson.
Sort of related question, which may sound a bit rubbish since I don't really know the physics or their scientific method at that scale, but were they doing enough experiments that they'd have eventually said it couldn't exist if they never found it for some amount of time? Or was it always something that could only be proven, not disproven?
Look carefully at this graph: http://www.quantumdiaries.org/wp-content/uploads/2012/07/Hig...
This graph shows how many pairs of photons were crated, classified by the energy.
There are a lot of ways to create a pair of photons, so there is a lot of background noise even if the Higgs Boson doesn't exist. This is roughly the dotted line (it's very difficult to see, because it's almost covered with the red line).
The black points are the actual measurements. They almost agree with the dotted line, except in the range of 125-130GeV where there is a bump. In that energy range there are more pairs of photons created than the expected quantity. The energy of the photons is essentially equal to the mass of the HB, but there are some dispersion because of the measurements errors and some quantum effects.
The red line is a simulation of how many pairs of photons would appear if the mass of the HB were 126.5GeV. They adjusted that parameter to get the best fit. This red line has a bump near 126.5GeV that is similar to the bump that the measurements have (black dots). The dotted line is very similar, so the red line cover it everywhere except in the bump range.
There is a lot of noise, so one possibility is that the bump is only a lucky streak, so they wait until they get a 5 sigma deviation, i.e. there is only 1/2000000 chance of getting a deviation as big as that form random fluctuations and noise. (The graph is old and shows only a 4.5 sigma deviation.)
The complete analysis is more complicated, but the general idea is that if there were no HB, they would get a different signal.