I don't think 'broke' is even the right word for that - I mean you can be a really experienced rider but still find some things make you nervous and as Darrin said if you're nervous that can make the horse nervous
To go back to my friend - she's been riding constantly for over 50 years, she's show jumped, hunted and done hunter trials but for some reason now finds riding on the roads on a horse she doesn't trust makes her nervous even though she could cope with more than most riders can.
I won't ride across or along anything with a steep drop to the side(s) because I'm afraid the gravity monster will reach up and drag me over so I get off and walk because I worry that my horse who isn't afraid will pick up on my nerves and start to think there is something to get worried about!!!
Now, we are starting to confuse rider confidence with the simple differentiation of a horse that can be ridden out, and one that becomes dangerous when asked to ride out.
I'll be the first to admit that at my age,, and double knee replacements, I'm not the confident rider i was in the past, and no longer will get on just any horse, have no more interest in riding studs, and I sure get a horse way more 'broke', then I ever did in the past, before riding that horse out .
I also would not think of now training colts, just in snowy fields, thus unsafe footing, as I did when younger.
That still have nothing to do as to whether that horse, with a good rider, can be ridden outside of some enclosed area. Has nothing to do with the confidence/experience level of the owner,, nor should that person feel that they 'have to ride the horse out, esp if that places them outside of their comfort zone,, thus making horse riding a dreaded task, instead of fun
I was merely defining as to what I consider a broke horse, and that has to be a horse that can be ridden outside of some 4 walls, if that rider choses to do so, without a major wreak!
Also trained for some discipline/ job, is not the same as just broke.