Tableau is representing your table as a hierarchy. The "leftmost" (on the columns shelf) field is your first layer of the hierarchy, and the next pill is the first sub-layer, etc. Thus when you sort on a particular column, you are sorting that column *within* the column(s) to its left. You can achieve complex nested sorts easily this way, but you do give up sorting where that sorting "breaks dependencies". The "another column" that you are right-clicking is, I assume, the first/leftmost column (or at least a column to the left of your sort-subject column).
One option is to do "Worksheet-->Export-->Crosstab to Excel". This exports the text table to Excel and the user can sort in a flat fashion. Works in Reader as well.
3 years after you posted your question, I am looking for the exact same thing...
Did you find an answer to sorting by columns header in Tableau ?
Thanks a lot for sharing your experience,