Please show where in those vids someone purposely sidestepped a punch.
That was your original argument; Sidestepping to avoid a punch, and countering. In those vids, the practitioners just slapped each other silly. There was no slipping or side stepping, just two bodies clashing into each other and swinging their arms wildly.
Actually kickboxing comes form muay thai, at least among the Japanese;
Kickboxing - Wikipedia the free encyclopedia
I don't know, that's something that should be discussed with the instructor of the school. The Relson school I learned from taught them. The Rickson school I attended after that also taught them. Royce's school in Hartford from which that video I linked is based out of teaches them. Rorian's sons also teach them.
Of course you did say that you only visited two Gracie schools....
Okay, but MY point is that Bjj guys will cross-train in MMA if they feel that they need more striking training, or to fill out holes in their game. Considering that there are Bjj schools out there that only teach ground fighting, I can understand that.
Okay, but I'm talking about what actually occurred, not hypotheticals.
And such basic wrestling lacks the benefits of formal grappling training. A woman with basic wrestling skills isn't going to be able to get a larger person off of her. Such as was the case with this woman in Australia.
A woman with a high level of training in grappling can get a larger person off of her.