This is all true, but the article isn’t about how long a photon thinks it lives or how much it experiences the passage of tone. It’s about whether the photon keeps going forever from the perspective of someone approximately at rest [0] in the universe (like astronomers on Earth!).

[0] General relativity has no preferred “at rest” frame, but the generally accepted FLRW model of the universe does. You can be at rest with respect to the universe, or you can be moving. If you are moving, distant objects in front of you will appear blue-shifted on average as compared to distant objects behind you.