On the first video, I thought the same thing as Danke42. It looked like the user hit the side of the knife and the log, causing the catastrophic failure. So sloppy technique + a pretty huge heavy baton, trying to split a pretty huge log. And like UCPOPO said above, I think that knife had a "corner" tang, not a round "radiused" tang. The corner tang is not as good because it concentrates force on a single point rather than distributing the force along a quarter circle. Cold Steel switched to a radiused tang for the Trail Master sometime after that video, I believe.
The second video, I don't know if the Recon Scout involved had the new radiused tang or not. Video date seems to be 2012, but he probably had purchased the knife a few years before. I would guess that it had the corner cut tang also.
Corner cut or radiused tang, I think the knives should be able to handle correct batonning. One thing not mentioned by anyone so far here, we don't know how much abuse those knives had gone through before the failures occurred. There is the phenomenon of "metal fatigue". All metal, including steel, will eventually fail if put under enough stress for a long enough period of time. Those knives might have simply reached their metal fatigue breaking point. They might look normal after repeated hard use, but small stresses eventually add up and cause a catastrophic failure. This is why I think it is smart to carry a backup knife on any extended trip where you'll be in an isolated location. You don't want to break your only knife when you don't have access to a replacement.
I don't think anyone can argue against the full sandwich tang being a stronger design. But it has its drawbacks too: significantly more weight, altered balance point and feel, wide thick handle, etc. The Trail Master and Recon Scout both have a significant tang going all the way to the end of the handle. Most blades throughout the history of knife and sword making have had tangs like the TM or RS or maybe even thinner "rat tail" tangs. Yet, with reasonably intelligent use, not even the rat tails broke very often, as far as I know.