It’s totally lame that they’d provide spatial data and a table with no common join field. Like the text says, they usually join on a “map unit”. It’s possible that the Value column in the raster is the map unit, but the table does not appear to have a corresponding column. The text also mentions using the column PRID in the table, but again there’s no corresponding value in the raster (which wouldn’t be the usual way to do it anyway, since the values of PRID aren’t unique but hey…) I have never used this particular soil data, so don’t really know what to advise. It sounds like you’ve done a lot of digging already, but that’s all I can think of, in case there’s a different table that contains the join field, or perhaps a field that’s hidden for some reason, I just don’t know.
~ Stacie