The increasing speeds of modern trains lead to excessive vibrations on the bridges, which have the potential to destabilize the ballast particles. The occurrence of this phenomenon not only increases the track maintenance cost, but can also disrupt the load path from the rail level to the bridge deck, posing a risk to the train running safety. The design regulations indirectly control this limit-state by restricting the vertical acceleration of the bridge deck. The assessments pertaining to this purpose often neglect the soil-structure interaction (SSI) effects considering that as a conservative assumption. Such effects can positively contribute by increasing the system damping, but they can also increase the bridge flexibility making it more susceptible to vibrations due to reduction on critical speed. Therefore, this study investigates the influence of considering/disregarding SSI effects on the ballast destabilization phenomenon using a probabilistic methodology. The results are classified based on the maximum permissible train speeds and the bridge span length. Due to the high computational costs of the reliability analyses, the associated limit-state is approximated by an ensemble of classification-based surrogate models using the stack-generalization concept. Subsequently, the upper/lower bounds of the failure probability in the presence of SSI effects are compared with those obtained for simply-supported bridges. It is pointed out that neglecting SSI effects for shorter span bridges may lead to an underestimation of system safety. For longer span bridges, however, this may lead to an overestimation of safety, which means that a non-conservative system can be designed.