Greek scales and names confusion????

One of the visitors at my http://www.ilhawaii.net/~lucy site sent me the
following comments.

>According to an article on Greece in the New Grove Dictionary of Music and
>Musicians, ancient Greek names for species of the octave included the
following (on white keys):
>B-B: Mixolydian
>E-E: Dorian
>A-A: Hypodorian
>D-D: Phrygian
>G-G: Hypophrygian
>C-C: Lydian
>F-F: Hypolydian
>Apparently, the Greeks counted intervals from top to bottom. When medieval
>ecclesiastical scholars tried to interpret the ancient texts, they counted
>from bottom to top, jumbling the information. The names on the table are the
>ecclesiastical names.

I checked back in Groves on scales,at the Westminster Music Library near
Victoria Station yesterday, yet am
still confused.
Can any of the tuning "experts" throw any light on this conundrum please?
For the complete letter please see
http://www.ilhawaii.net/~lucy/lsd/corrections.html

TIA
Lucy
http://www.ilhawaii.net/~lucy