Yeah, I don't really know what was up with the flyer thing. They should have done it for all or none. I don't like the idea of discarding some shots as fliers or taking 80% groups in most situations. Usually that "flyer" is just a part of the group and over many rounds wouldn't look like much of a flyer.
Some of it could be human error, but there's also the issue of 3 shots not being a representative sample, which is what they're trying to demonstrate. They didn't really go into the statistics in that video, but this video touches on the statistics without getting deep into the math:
If you want something that's a pretty lomg and dry read but goes into everything from group size to why discarding flyers probably isn't a good call this article from PRB and the other articles they link to cover it all pretty well:
This article is going to dive into the most effective ways to quantify the precision of a rifle and...
precisionrifleblog.com
The other glaring issue in the first video is the use of ammo that is, by their own admission, sloppy. That likely had a negative affect on the consistency from one group to the next. I also wish they would have created an aggregate group from each group size for comparison, which should have made it clearer that small groups don't provide a representative sample. In all likelihood there would be little to no difference in the size of the aggregate groups.
If you can ensure your groups are shooting to the same point of impact or overlay your groups into one big group multiple 3 shot groups work well. I typically use Photoshop to overlay 3 or 4 3 shots groups when I want to do that, or I'll shoot benchrest card and overlay all the individual shots. Ultimately that's the same as shooting a single larger group, but it's easier to test a load over multiple days and ensures you don't shoot out the point of aim.