Should my best friend and ex-boyfriend be talking as friends?

My ex-b-friend and I broke up over a year ago but have been friends since then.... until recently he admitted he still has feelings for me and needs to not see me for a while to try to get over me. Since then I've learned that he and my best friend have been talking and consoling one another. She recently also broke up with her boyfriend. I know they will never try to be together... they're not like that. But I feel isolated and betrayed by both of them. I let my best friend know I didn't like her talking to the ex but she continues to talk with him. Who's right in this situation?