Gamblers fallacy is about independent probably - there are cyclical natural catastrophes.
That sounds very made up.
So the notion was certainly a reasonable one even if not ultimately true.
The Wikipedia article mentions 26 million year intervals. So we're probably good for another 10 million?
[1] https://en.wikipedia.org/wiki/Nemesis_(hypothetical_star)
(And to note: I can't edit my reply now but I read 'there' as 'these'. Obviously there are other (somewhat) cyclic natural catastrophes especially on shorter timescales.)