Nah. Let's start at the top and work our way down.
1. Qomolangma (Everest) Female. "Mother Goddess"
2. K2?? - "...just the bare bones of a name, all rock and ice and storm and abyss. It makes no attempt to sound human. It is atoms and stars. It has the nakedness of the world before the first man - or of the cindered planet after the last"
—Fosco Maraini
3. Kangchenjunga (I can't determine a gender) "Sacred treasure of five snows"
4. Lhotse (appears genderless) "South Peak"
5. Makalu (male by inference - see SP Makalu page) "Big Black"
6. Cho Oyu (Female) "Turquoise Goddess"
7. Dhaulagiri (no apparent gender) "White Mountain"
8. Manaslu (no apparent gender) "Spirit Mountain"
9. Nanga Parbat (No apparent gender but I'm putting this down as female for obvious reasons
"Naked Mountain"
10. Annapurna (female) "Full of food" (apparently a femine sanskrit construct. Usually translated more poetically as "Harvest Goddess"
11. Gasherbrum 1 (No apparent gender, but maybe the Balti language uses male and female adjectives, I dunno). "Beautiful Mountain"
12. Broad Peak (does this even require a comment?
)
13. Gasherbrum 2 (see Gasherbrum 1)
14. Shisha Pangma (No apparent gender in either it's Nepali or Tibetan names) "Holy Mountain" or "Mountain overlooking a grassy plain" - see SP page)
So I make that 2 female (unless we we allow Nanga Parbat and Broad Peak), 2 male and 10 genderless names.
If my survey sample is sufficient, I'd have to say that the myth in the OP is
BUSTED!