The article mentions the photon sphere, but is there any source on "orbit multiple times before escaping"? My experience is just in Kerbal Space Program, which is a 2-body approximation, but afaik once you are in orbit, you can't escape without changing your velocity. Also, 180 degrees is the exclusive limit of a gravity bend; less than 180 is not an orbit, but as soon as you reach 180 degree bend, it becomes an orbit.
Of course, with 3-body things get much more complicated. For a third body to pull photons out of a photo sphere, fascinating and I can imagine it happening, but I haven't seen any sources along these lines.
With all of the mass inflow there is likely a very turbulent gravitational environment just outside of the event horizon. This could be sufficent to provide a little transient local lensing to kick a photon back out (or in).
Of course, with 3-body things get much more complicated. For a third body to pull photons out of a photo sphere, fascinating and I can imagine it happening, but I haven't seen any sources along these lines.