It's impossible to logically disprove a theory like this, because the entirety of your thought process would itself be a random fluctuation, never mind the inputs on which it is based.
The problem is that if you start with the reasonable assumption that you objectively exist and that your observations are valid, the model of the universe derived from those observations (or at least some otherwise viable models) includes prevalence of Boltzmann brains.
The problem is that if you start with the reasonable assumption that you objectively exist and that your observations are valid, the model of the universe derived from those observations (or at least some otherwise viable models) includes prevalence of Boltzmann brains.