I also have no problems with my husband's old or new female friends. I know them (2) and I know there is nothing going on. I trust him. He calls one old girlfriend every once in awhile (about 3x a year) to catch up or vice versa. We've had dinners together (our families, 2 wives, 2 husbands) when we visit their state. Totally cool.
This particular situation - HELL NO.
This woman is being completely inappropriate. Why exactly does she keep asking him out to lunch, dinner and now a MOVIE!?!?! Sounds like she's fishing for a date and doesn't care if he is married or not.
Is this a working meeting? Why would she need a working meeting one-on-one, with the principal? She doesn't. So I suspect something else.
He should cut this short, like the other posters said. Or be blunt. What is this meeting for? And wait for her answer. If it's a school situation, then there should be a witness. PFA president or something. Other staff member. There is no reason for them to be alone together. (If, however, they have a working, professional relationship and end up having a friendship, fine. But even then the WIFE would have to be OK with it. This is not what's happening here.)
If not, there is nothing to meet for.
I would never in a million years ask (pester with texts, phone calls, emails) my school principal (male or female) for a one-on-one lunch, dinner or a movie.
She sounds like a stalker at this point. Totally inappropriate. He needs to establish firm boundaries.
Your friend's wife sounds like a sensible person. But this woman doesn't sound kosher, so I vote no way.
HAVING THE PRINCIPAL's TEXT
Could be perfectly innocent. I had my male principal's text because he called me at home, left a message about my son and it was on the caller ID. People live on their Black Berries and smart phones and so answer emails and call parents back if it's that important. So I would not automatically jump to the conclusion that something else is going on.
I would never text him directly unless the school was on fire.
I would have no reason to text him. As a hard working principal, he's already dealing with a million little things and doesn't need that intrusion. The only people texting him should be his wife and immediate friends/family.