Well Ken I really SHOULD be more careful about the nomenclature of tunings, BUT then again what about the E9th and the C6th, both of which have theoretically incorrect names ?
Just for fun --------------->
Tuning are named by the chords they contain ! (You've already pointed that out

)
I believe that E9(maj7) or E9/B, and F Maj 69 or F maj9+6 would be more correct ?

Well no ninth chord contains a major seventh, so obviously E9th is incorrect and if one goes down the "E9th Chromatic" road that's a VERY slippery slope, as Chromatic means:
chromatic |krəˈmatɪk|
adjective
1 Music relating to or using notes not belonging to the diatonic scale of the key in which a passage is written.
• (of a scale) ascending or descending by semitones.
• (of an instrument) able to play all the notes of the chromatic scale.
And we are missing so many of the chromatic notes within the tuning: F, G, Bb, C, C#,
And C6th is completely wrong as the bass end has an F in in the bottom two strings set the ilk for the following notes, and infer "F".... So logically based on the F, one would conclude that C, F, A, C, E, G, A, C, E and usually D....... gives us the notes of Fmaj, (Root, third and fifth) plus we have maj 6, maj 7, and maj 9 notes, the choice is either to base the name on the 6/9 or the Maj9, either way would be much more correct than C6, because there is absolutely no precedent for using the name C69 sus4, and a sus 4 on the bass is absolutely out of the window theoretically.