I found this piece on saturday also. It sure looks like the base of an Agate Basin. The base and edges are ground and the shape is there.
If it was broken during reduction stages (which looks highly likely), than the grinding is probably due to edge / platform preparation. In other words, it broke on them while making it. Any knapper will tell you that it's common (usually followed by a few swear words).
How thick is this piece? The last pic you posted gives it the appearance of being at least 3/8 inches thick.
It shows a strong 1/4 inch thick
Okay, a strong 1/4" thick is more like it and would be within the
range of the specimens from the Agate Basin type site.
It could be as Neanderthal suggested, broken during reduction.
During the reduction process I was under the impression grinding
a location was done just previous to the next flake removal. So,
not being a knapper I am wondering if it was a common practice
to grind all three surfaces, (the base and both basal edges) all
at one time before proceeding with the reduction sequence.
I believe you stated all three of those surfaces were ground.
In initial cobbling and reduction stages you always have to focus on deltas and isolate those platforms, but when they get to this stage it's quicker (for me at least) to abrade the whole side, sometimes around the whole perimeter before whacking. It just makes things a little more speedy and efficient when you have an abraded, consistent edge to work with. I have a few aboriginal pieces that have the whole distal end or a side abraded, I assume it's due to resharpening preparation.
I know some knappers who abrade the piss out of everything (even the faces) before running a row of flakes, almost to the point of being FOG. I've also noticed some aboriginal knappers practiced that as well, I have seen several (especially to the east) Clovis points that exhibit heaving grinding / abrading on the face.