Well, what I am going to tell is may be not applicable to your horse, but my horse has the same. She has not been mistreated.
She is not easily scared by things she can see or things she may touch/sniff. In Kyra's case I think she doesn't like to be pressured (someone walking/biking behind her gives her the idea that she is "driven" /driving game), so I let everyone pass and then it is all right. Or may be she doesn't trust moving objects she can't see. She has no problem if I walk behind her (e.g. With long reining).
Today I had my first trail ride and I could not get her to walk next to her paddockgirlfriend. So we walked 2 meters behind.
In the arena I almost ride/work alone or on the other side so I haven't mentioned if she's scared in the arena too, if some one is riding behind her.
If she is scared of other horses walking behind her, it can be a hierarchic issue: that she is not walking in "the right place" according to horse rules.