I gotta strongly disagree with this. The root of the chord is not determined by what note the bass player plays, and conversely, the bass does not play only the roots of chords. If that was the case a walking bass line would change chords with every note, and it does not. If the chord is G and the bass player plays B, the chord is still G, its just an inversion with the 3rd on the bottom. Basic classical music theory teaches it this way.
However if the chord is G and the bass player plays an E, the chord is heard as Em7, because the bass is adding a new note to the chord that does not fit a G. But that same E added as a higher note, perhaps in the guitar chord (or perhaps as part of a bass run) it might just color the chord to a G6. There are no hard and fast rules, but consider this: a good guitar player rarely plays full block chords, and frequently omits the root leaving it for the bass player to provide.
In jazz, the guitar (or keys) frequently plays chords made up of the notes that most define the extended chord function, playing mostly the 3rd, 7th, 6th, and 9th of the chord. The root and 5th are the same note for most chord functions and do little to defining the function so they are usually left out.
The perceived chord is dependant on the context, the key, the scales being used, the surrounding chords, etc. Given the right context, a chord is heard clearly without the root being played at all by anyone.