When Harry Met Sally

Can men and women be friends...just friends?  I have been thinking about this a lot lately because it has come up. Last night, I sat in Bible study and listened to Beth give the characteristics of a close friendship; I had very few relationships that fit but one of them was with a guy. Troy quickly and emphatically always answers the question no.  He says a girl can be just friends with a guy but a guy cannot be just friends with a girl.  I can think of 3 times in 3 completely different contexts that he has said that this week.  Like I said, it has come up.  I have issues with that...big ones for a couple of reasons.
First, I have always found it easier to be friends with guys.  Guys use and need less words than women which suits my personality.  I hate small talk.  I am not good at it, and I find little use for it.  I am also naturally very shy.  I don't feel a need to fill quiet space with words.  I can sit with a person, say nothing and be satisfied.  I am very much like my dad in that way.  I will dig deep with you easily and quickly...which is why I love Bible study so much...but day to day little stuff...eh.  Guys are ok with that.  Women want to talk about everything, anything and nothing.  Also, I have very little tolerance for drama in my own life.  (I will listen to yours, but I don't need any of my own.)  I know not many women will say they want drama but, man, a group of women always end up with it.  Y'all know the games women play...they way they manipulate and all that.  I can't deal.  Men just don't tend toward drama the way women do.  There is also the side note that for at least four months out of the year the topic I will most want to talk about is college football.  So, I find it easier to really be myself with guys.
Second, I am very secure in my marriage.  I love my man.  There is no wavering in that.  I am not swayed by anyone else.  I can appreciate a good looking man and even can be flattered if a man is paying attention to me, but it would never cross my mind to cheat on my husband.  We have fought too hard for our marriage to think of it that cheaply.  I know affairs can creep up out of nowhere and happen on a slippery slope, but nothing about who I am wants that emotionally or physically.  My heart is taken.  I don't have it to give away to anyone.
But you know what, I may just be proving Troy's answer to be right.  I have never been a man.  He has.  He knows what a guy feels and thinks...how they act and react.  I explained how I feel from a woman's point of view.  It's possible...but that's what Troy said.  It's the guy that can't do it.
What do you all think?  Can men and women be just friends?  How about 2 happily married people?  Can they be friends with someone else?