Who says? And are they qualified to pronounce on this particular OP? Find out before you post.
I do - I am a professional scientist.
The fundamental problem with the assertion in the OP (amongst many others) is that assumption that an improbable event cannot occur, simply because the probability of it occurring is low. That is non-sense.
Take this simple example - the probability of rolling 6 sixes on a dice in a row is 6 to the power 6 or 1 in 46,656 (I believe) which is very small. But then the probability of any other specific combination of 6 throws is also 1 in 46,655. According to the poor thinking of the OP if you roll the dice once per year it would take 'on average' 23,000 years for 6 sixes to come up. But then every other combination also has the same probability so the OP assertion would claim the same (on average they'd come up in 23,000 years) too. But of course we know that to be non-sense, because the very first throw will produce a combination with a 1 in 46,656 chance, as will the second and so on. So the notion of 'average' time to achieve a particular outcome really means nothing as that outcome is just as likely (or unlikely) in the first 'throw' as in the 46,656-th throw.
What the OP seems to be claiming is the equivalent of saying that if you only throw the dice 20,000 times (i.e. less than the 'average') then the likelihood of throwing 6 sixes is zero - it isn't and to suggest it is is totally muddled thinking.