"Loose" horse?

Today's ride was interesting.  I thought it was going to be a quiet, quick ride.  And it almost was.  On the way back, by "grand central station" I heard galloping hooves coming up behind me.  Zoe and I turned around in time to see a riderless horse galloping towards us and then turned left to go up the ridge to my left, followed by a horse and rider that seemed to be chasing the first horse.  I wasn't sure if the first horse was being ponyed and got away or if it was a rider that rides and lets the 2nd horse go loose all the time.  I've heard that some people do that with their older horses.  I've even run into a man once that was doing that but the "loose" horse stayed with the mounted horse.  I've even done that with foals out on the trail…but the foals tend to stay with their dams.  Anyway they disappeared up to the top of the ridge and I continued down the trail.  I got to thinking that maybe it was a "loose" horse and it could be a rodeo in front of me, so I got off and walked with my horse.  Zoe was doing ok.  She kept looking up the hill towards the 2 horses that ran off, but otherwise she was fine.  As I rounded the corner, the ridge trail mets up with the trail I was on and I met the 2 horses again.  This time the rider had the "loose" horse on a lead rope and was getting her horses arranged to continue on her ride.  I asked her if she was ok and I got a short "yes" and off she trotted.  This time her ponyed horse was trotting behind her-a bit wild but following.  While I was talking to her a bicycle rider and a dog came up behind Zoe and me…they stopped and he made the dog stop and sit next to the bicycle.  Very polite bicycle rider.  Much nicer than the horse lady.  Maybe the horse lady just had a bad experience and wanted to get home quickly.  I'd like to think that was the situation.  If she is one of those people who let their older horse go "loose" on the trail, I'm not too happy with her.  Either way I'm glad the "loose" horse didn't chose to run up to us or blow past us on the same trail.  Seems like a recipe for disaster.  And I'm glad she got her horse on a lead rope.   Zoe was a bit excited so we walked for a while.  After a while I got back on and rode home.