I think this is what the parent comment is getting at.
How are you supposed to build a model of a black hole given the source is universe-scaled and the time-line for receipt of any particular photon is probably(?) vast and our observations are distant.
It's an incredible fact that one can do this -- predicting the properties of the photons emitted at the very first instant that the universe became willing to allow a photon to propagate freely.
A young Randall Munroe could have picked from a number of really well-motivated reasons to state, "Science, It works...", but he picked this one: https://xkcd.com/54/
Modern precision cosmology works really, really well.
Still, I have a sneaking suspicion we are making flawed assumptions because our observations are from this point, and only this point, in space and time.
Just my opinion, and it’ll probably turn out to be flawed itself like most of my opinions ;)
> Does anyone assert that any photon carries information about what it interacted with in the past?
Yes. I do. The Cosmic Microwave Background encodes structure from many foregrounds in its wavelength, polarization, and momentum vector. Moreover, if one is able to build a well-motivated model for the photon's source and path of propagation, one can extract still more.
Grab a linear polarizer and play with it while you look at the daytime sky. The light you see is polarized differently depending upon the path it took to reach you from the Sun.
Look at your hand. Does the color of the light that reaches your eye not encode a convolution of the emission spectrum of the nearby light source and the reflection spectrum of your hand?
Regarding the black hole question, I'm no GR expert, though I am a professional gravitational physicist, but my guess is that the photons that make more orbits emerge from closer to the event horizon. The article discusses a notion of "shells", so I surmise that there may be favorable resonances in the photon-scattering cross-section at integer orbits.
Scientists are occasionally wrong about something, sometimes in spectacular ways, but when multiple scientists at top institutions all agree about a few basic physics concepts in a popular-physics article, there's a pretty good chance that they know what they're talking about.