Pure motion captured data?

Yes, motion capture.

There isn't really processing applied to it.  The adjustment sliders are just changing curve values assigned to the different motions.  Some of those custom changes that you make might force the curve into "unnatural" territory, but maybe some people want that.

Any BVH data can be manipulated by changing the range to which the capture is mapped.

Changing the anchor values, the capture values, or the timing value ranges can give you a variety of choices. 

The capture may appear differently on different geometry.  Download the data without making changes, and look at the animations without geo.  I think you'll find what you're looking for.

stop motion is where each point on the slider is moved by hand... motion capture is where you record an actor and copy that data to your model

your understanding of pure motion capture editing is wrong and yes you can use a slider but Mixamo is mostly made with stop motion... there may be 1 or 2 made with motion capture but I'm not aware of any

you can of course convert Mixamo models to use whichever system you need as well but in general you are best to use one or the other instead of mixing them