Perhaps Hunter was mistaken by using host in the past tense instead of could host. I have not researched the history of the JFK to see if VTOL aircraft ever landed or took off from the ship.
No, the issue was your earlier claim:
"We are flying Harriers off the JFK now. Probably part of a Marine Aircraft Wing."
Which is incorrect. Whether or not Harriers could be successfully operated from a CV or CVN was answered in '76-'77 when VMA-231 deployed aboard the USS Franklin D. Roosevelt as part of CVW-19 for a Med cruise.