This is a bit of a weird story and I'd like to know the facts behind it because the overtones do not quite chime with my own experiences.
Most women in Lebanon do not wear the hijab. For a start, a lot of them are Christian, but even Muslim women do not particularly cover their hair (voluminous hair styles are big in Lebanon).
The women that tend to wear a headscarf are either Gulfies on holiday (they tend to wear abayas and niqabs as well, but they are very few and far between), old rural ladies who wear what you might call the "Anatolian style" of headscarf (which you find across the region and isn't Islamic at all; it's the equivalent of the Queen and her headscarf or your gran wearing a rainmate), some Sunni muslim middle-aged women (who tend to wear white scarves), and Shia Lebanese women. Even then, I think it is a bit disingenuous to consider Lebanese Shia headscarves as "headscarves". The last time I was there, all the Shia girls in Beirut were wearing bright dayglo pink scarves with matching nail polish and lipstick. It was about as religiously conservative as a glitter bomb.
And the thing is that I'm pretty sure I was invited into a Sunni mosque in Beirut with my hair uncovered, and no one had a problem with it at all. They just wanted me to admire some of their tiles.
Lebanon is not a "stereotypical" Middle-Eastern country in that sense. Beirut is like a mix between Paris and Alexandria in the 1950s with an added dash of Miami circa 1985 and a bit of early noughties Athens to boot.
Indeed, Beirut is one of the only places I have ever been where I have gone out on an evening with my hair and nails done, my glad rags on and a full face ... and still felt like a bag lady compared to the women around me. 
So this story kinda doesn't chime with me. If the grand mufti of Lebanon refused to speak to any woman who didn't have her hair covered, then I can't see how he'd be able to even cope with walking down a Lebanese street.
Very odd. Very odd indeed.