The "stopping rule" is valid in cases where in any given trial, you "stop" on a success. This leads to the average trial having more "successes" than failures. This is best explained by, again, heads and tails. You succeed on a day when you flip heads, but you keep flipping on tails until you get heads.
Some days you'll get just one head. Great!
This is supposed to skew the data against Dream, because it unfavorably makes the odds worse for him. The problem with this "stopping rule" is that it doesn't change the base chance of success. If you run this heads and tails simulation, you aren't going to magically have a more than 50% of head drops because you stopped on heads. The coin is still 50-50.
In the streams, piglin barters don't stop. Perhaps gold is not further traded, but the ender pearl rate is still .0473. New runs are made regardless. On a personal best record, maybe on a run with 3 pearl drops out of 10 gold is earned, and Dream shuts off a stream after a good run. That doesn't change the fact that there are more streams. In the case of the last stream, unless he got ungodly luck on only the last run of the last stream would this "stopping rule" be implemented. And only then would the stopping rule apply. But this luck was consistent across all 6 streams.
The six streams in question were all watched and tabulated after Dream's short hiatus. There was no specific stream the moderators picked and chose, but simply all of them. The added streams should not have been calculated in the result because you're changing the sample. Introducing new data in light of the improbable is misleading.
Even then, the stopping rule and added data went so far to decreasing the 11 leading zeros to... 7 leading zeros. For reference, statistically significant is still .05. 1 in 10 million odds is still unquestionably difficult. Someone has calculated already how many alternate universes it would take for every man, woman, and child playing a stream's worth of runs a day since Minecraft came out to attain his luck.
I'm incredibly disappointed, first and foremost. There are skeletons in everyone's closet. I have my own, and so do many. But please don't try to kill math and science by obfuscating the math. What happens when people use it to their own advantage, and there's no trust remaining in them? People lose faith in them, and go off uninformed opinions.
Maybe you don't agree with this side comment about the stopping rule and the added streams. That's fine. I just implore you all to do the math, and understand that there are some things which shouldn't be lied about, like math and facts which everything else relies on.