Is it correct to say "running in the rain"?
According to Oxford dictionary and all the other dictionaries I came across, "In"always refers to someone or something (still or moving) that is surrounded or enclosed by an area.
I think you have misunderstood the dictionaries. The rain is the thing that surrounds the person who is running.
In = inside or within. (Occasionally, it is used as a short form of "into")