Thanks for checking into this some more, Robert.
Yes, the Help Doc is a "little more clear", but still not great.
At least it does mention the "Input Table X and Y coordinates". However, I think the missing term is "define".
In other words, is this not essentially the same thing as the "Define Projection" tool?
And, I think you/Esri has to be careful using the term "spatial reference information", because from my perspective a Standalone Table does NOT have a defined spatial reference; rather it is unknown!
That said, there is inherently some "coordinate information" in the Standalone Table with X and Y fields, but that is different than the almighty "spatial reference" which is much more comprehensive information that is embedded in a spatial layer.
I do understand, however, that ArcGIS attempts to interpret the coordinate values to at least "field match" the X and Y inputs. And, sure, a Standalone Table could have another field with the "coordinate system" info, but I don't see how ArcGIS would know to read that because it could be any field name, and there are way too many variations of coordinate systems written many different ways. So, I don't see how it would be possible for ArcGIS to automatically determine and define the Coordinate System/Spatial Reference of a Standalone Table.
It seems to me that it CANNOT, so it just defaults to the Geog/WGS 84 -- which I don't like either, because I think it's misleading, and sort of a wild guess.
...However, if I'm missing something, please let me know. Thanks!