Billy rings are fixed-position ... you cannot move them up and down with respect to the webbing. They are therefore considered potential entanglement hazards. They are usually welded to the slider that attaches them to the webbing. Billy rings do stick out at a 90-degree angle to the slider.
There are other, angled rings that are also welded or otherwise permanently attached to the slider. These are typically not called Billy rings, but they still are not DIR, because they are rigidly attached, stick out at an angle, and are considered entanglement hazards.
Bent rings attached with the standard slider are ... as far as I know ... OK. As I said, my DIR instructor didn't seem to have any issues with them, and he looked over our rigs pretty closely. BTW - the plate and harness I used for class were from FredT, although I also have rigs from Oxycheq, and Dive Rite.
There are at least three DIR instructors on this forum ... I'd like to hear from one of them on this topic. Not that I think it's a deal-breaker, but they always have good explanations for why they choose the gear they do.
... Bob (Grateful Diver)