Should I trust my boyfriend's 'friend' isn't really an unresolved ex waiting in the wings?

I think you feel threatened by this girl but that telling your guy this will likely do nothing. All you can do is trust him. Trust that they are just friends. The more you worry about things the bigger the problem with become in your mind. She has a boyfriend. Granted he is inattentive and your guy is the one she calls to talk about things. Tell me how did you find out that her boyfriend is inattentive? Did your boyfriend tell you about their convo? If so he has nothing to hide and is letting you know you can trust him. I have been in your shoes before. Chances are that this chick may very well want your guy....The point however is that your guy wants YOU. And that is why he is with you and not depressed friend.