I definitely think it’s a relative term, and I think I’d agree with the people saying that “honest” is probably a better term than “safe.”
I have a three-year-old OTTB who is very honest and will take a joke. We aren’t doing much right now because baby, just light walk-trot work with some poles thrown in every now and then, but we do hack all over the farm (in varying degrees of daylight, with deer everywhere/coming out of the woods left and right when the sun starts going down). He does spook on occasion, but it’s always genuine and the worst of it is usually just a few quick steps sideways. All I have to do is close my leg and sit back and he might go “Mom, are you sure?” but as long as I’m right there with him, he’ll move forward past whatever spooked him in the first place.
Would I put just anyone on him? No. He’s three, his balance is questionable, he’s wiggly as heck, steering is eh because we’re still figuring out the whole inside-leg-to-outside-rein situation, and he’s not the greatest at carrying himself right now so he can use some help with regulating his pace. I wouldn’t put an inexperienced rider on him unless all they were doing was walking around on a lead line with me right there on the ground.
Does he pull dirty tricks? Also no, he’s just a baby and he needs someone with experience on him right now. He’s an angel on the ground with my barn owner’s daughter (who is also only three - we obviously don’t leave her alone with him unsupervised, but she always says hi to him first thing in the morning when she comes up to the barn and he’s always more than happy to get cuddles from her), he’s been great with other kids running around, and while he might greet new things with some skepticism, he always listens to me when I encourage him to keep going.
Is that safe enough for me? Absolutely. He’s honest, he’s got a good brain, he listens to me when he’s not sure (which will be an absolute asset for cross-country, since I want to turn him into an eventer), and that’s what I was looking for (and I bought him sight unseen off the track except for photos/videos and a pretty low-key vet check, so I think you could say that it worked out alright).
Of course, my first lease horse had a rearing problem when I first started riding him (it was a fear thing courtesy of a previous owner, we got through it because I was a naive pre-teen who loved him and wasn’t frightened enough for it to overpower how much I adored him before we could solve the problem), so most horses feel pretty safe compared to that at this point.