<human>: Can you condense the text into three sentences or less?

Lemme tell you guys a little back story. It's a classic friendzone story. I started going out with my girlfriend, her bestfriend confessed to her, she rejected him. 

About a month or so ago, my girlfriend and I had a conversation about her talking a lot to her best friend since they pretty much text each other every single day. (Not as much as we do but it's still very well throughout the day) She currently still talks to him everyday but less than how much she usually did. 

Now onto the problem. She's shown me her conversations with him (Don't worry I didn't ask because I'm nosy, but sometimes we had another problem where she voluntarily showed me her messages) She trusts her best friend a lot since they've been like that for about 5 years now so she says that when he tells her he likes or compliments her, she knows that he doesn't mean it and "he cares for her happiness more than his own." Another part about him is one time, he basically said he'd be willing to be her rebound if her and I ever broke up. Is that really something I should be worried about? 

It just bugs me about how presistant he is. I for one have faced a similar friendzone problem but I was never on this side so I don't really know what to do. I don't wanna break up their relationship because I'm not that kind of a guy but idk what else to do.

Also just for clarification, he does NOT try to ask her to hang out and stuff. He kinda just sneaks it in there, i don't really know what they talk about.
<bot>: My girlfriend's best friend is being presistant after being rejected and sometimes says that he still likes her and stuff. I feel pretty bugged by that.