Well, why do you get defensive about it? I get that nobody wants to be with a psycho that gets jealous over everything. You guys can disagree on things sometimes, but honestly I have been with my bf for five years and I love him and trust him more than anything. If he was talking to a pretty girl, friend or not, I would probably get a little jealous if I heard them laughing. If they were both agreeing on something that I disagreed with, you have to at least understand that when there is a pretty girl around that seems to relate with you more, it’s easy to see them as a threat even if you are the most reassuring person on the planet. If I get jealous, I do not always mention it because I know that at times I can make a big deal especially when I’m PMSing, luckily my boyfriend never really talks to girls anyways. 
She seems to love you and is being honest with you about how she feels, she is clearly feeling hurt and insecure in some way. I think that it’s best if you try to control your defensive feelings. She probably isn’t trying to offend or be controlling, she just feels a certain way you know? 
If my boyfriend is ever bothered, I try to imagine myself in his shoes. It helps me understand his position more. Imagine if you were feeling jealous, you know? Wouldn’t you tell her? How would you feel if she was offended by that? 
I know you said you shower her in love and all that. I think this is probably one of the best times to do that, and show her that you can at least understand where she’s coming from. 
Let me know, I’m no expert just a random person.