Humans have a hard time accepting true randomness as even being possible. A famous example being Einstein's criticism of the emerging claims about random behavior at the quantum level "God does not play dice with the universe." Many people really, really want the universe to be this ordered, deterministic, machine. It sounds like the same goes for whatever old Buddhists cooked up this doctrine that everything is dependent on conditions.
I observe that this statement is true, at a practical level, most of the time. In our ordinary day-to-day lives, it is accurate. The conditions into which a person (or animal) are born will have tremendous impact on how they turn out. The conditions under which one undertakes any task will similarly have tremendous impact. So, that's probably the focus of the observation here (though I am not a Buddhist and don't actually know what they were getting at).
There have been some serious attempts at injecting determinism back into quantum mechanics (such as the "pilot wave theory") but they bring their own problematic side-effects and are not in mainstream scientific acceptance. Be that as it may, legit challenges could be made against this claim of "true randomness" from this interpretation (or other rival interpretations that give us our determinism back). The Copenhagen Interpretation has the highest level of scientific consensus, and it would predict true randomness, but this isn't something that has been definitively proven (especially in the case of serious rival interpretations). So, it may turn out that the Buddhists are right, here, though they don't have any proven scientific basis for making that claim at the quantum level (yet).