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[OngBonga]

So their argument is that photons from distant events are red-shifted not by universal expansion, but by "bleeding" energy into the intergalactic medium.

Can redshift not also occur as a consequence of moving out of a gravity field?

[MadMojoMonkey]

Can redshift not also occur as a consequence of moving out of a gravity field?

Yes.
Hubble accounted for this when analyzing the spectra of distant galaxies.
The word "distant" is poorly defined, but relevant, here. It's not that all galaxies are distant, and he's studying galaxies.

The Hubble constant (actually Hubble was first to confirm it; it was hypothesized by Lemaitre) increases with distance. At "close" distances (lol), the local motions within a galaxy are like a mask of white noise through which it is hard to pinpoint an exact "general motion" of the galaxy. I mean... there are wide error bars on that value, because the internal motions of the galaxy are on the same order of magnitude as the recession velocity. When you look at "distant" galaxies, the local motions are about the same as the close galaxies, but their recession velocity is now much greater than their internal velocities. This allows a sharper resolution (finer error bars) on the measurement.

The mass of the galaxy is taken into account, but with galaxies of relatively equal mass, this is a wash.