He calls is ex his "best friend" now. They are really really close. Is this something else?

I started dating a guy about a month ago and have increasingly been concerned about the relationship he maintains with his ex of 20 years. He says that today they are simply “best friends”. This new label includes cooking dinner for each other, going on trips, and even sleepovers. Last night I was at his house getting ready to leave when the phone rings and it's the ex. He takes the call in another room and I hear him say “Hey, baby….”. A friend of mine says I shouldn't worry because he calls everybody baby. What do you think? Is this guy trying to be shrewd by simply relabeling the relationship with his former lover of 20 years?