The physicist involved are also skeptical of their own experiments. That's why they independently build two experiments, ATLAS and CMS, that measure the decay product of the collisions (in addition, they are also a number of other more specialized detectors).

The design of these detectors are rather different, and they are build by different team, yet are are giving consistent results.

So of course they are common assumptions, but they did do their homework to try to mitigate this.