You know I think this might also be a case of the time too....
When I was a kid I volunteered at the stables I took lessons at, this stables was huge! There were 25+ barn owned horses (they were a trail riding facility/rental horse facility, they gave lessons, pony rides,trail rides, held rodeos, and had two additional barns for borders) it was a military run stables on Camp Lejune
in NC (today the stables is still there but there are no more rental horses it is all privately owned borders, what I'm about to talk about is the middle picture on the last row of pictures on the link above. It definantly looks different than it did when I hung out there, now half the poles are gone and it no longer has a dirt floor.). I was one of many 'barn rats' that spent all of my free time at the stables. They had most of their horses hooked to a line during busy parts of the day, quick release clasps, short leads on a row under a perminant canopy/open barn (for a lack of better words). The lines were hooked to parallel poles driven into the ground. Anyways I, along with many other kids ranging in ages, were aloud to be all around these horses, under them, on top of them, behind them, between the bars what not. We were sort of supervised by employees, when ever they walked by while doing their various jobs. NOW this would never ever happen in todays stable, because of the liability issues and the lack of trust, that children know what to do if a horse has a problem.
SO I'm thinking that while you look at these pictures you have to remember (unless you are alot younger than me, and I'm really not that old at all) that it was a different time. I'd take it with a grain of salt and just be smart about what you (general you) decide to let kids do around the horses you own, whether its a stud, gelding, or mare. Every horse is different and lets just hope that you know your horse and you know who (and their ability)you choose to be around it. That's my two cents regarding the OP.