loss,
It might be fruitful for you to enumerate examples of that which the truth movement considers to be within the scope of what you call "low probability" events. Doing so would allow us to be a bit more specific about what the truth movement may be right about.
Generally speaking, when something is considered to have a low probability of being true, then, in such events, a greater proof requirement attaches precisely because the event is improbable to begin with. That would be true for low probability events occuring on 9/11/01 and on 3/2/10 or on any other day, correct? Furthermore, I don't think you are claiming that the "9/11 truth movement" is obliged to also take on a responsibility for questioning all other low probability events that have occurred before or since 9/11, are you?
Overall, what the truth movement may have gotten right in the general sense is that the "low probability" events of 9/11 were not only never explained with a greater reliance on proof -- based on the improbability of occurrence -- but, for that matter, were never really explained at all in some instances.
Noteworthy as an example of this phenomenon of little or no explanation is the 9/11 Commission report's failure to mention that WTC 7 pulverized itself on the afternoon of 9/11. I am not here saying no explanation of the event was ever offered, for we know, of course, that NIST took a stab (literally and figuratively) at explanation in 2008, 7 years after the event. But, the 9/11 Commission report did not even mention the event, let alone offer explanation.
That it then took 7 years to even offer an explanation, separate and apart from assessment of the validity of that explanation, should rank, I think, as an historical red flag that says something about this generation of inquirers and citizens.
all the best