In the special relativistic setup in your final sentence, the spaceship occupants could in principle watch our clocks and observe that ours are ticking slowly, with the same redshift.
Observers at a high cosmological redshift cannot watch our clocks at all. They can only look at the even more distant past of what will become our clocks in billions of years, and there's no reason to think that the redshift we ascribe to them is the redshift they ascribe to our precursors.
(Indeed the gravitational redshift from the metric sourced by Earth (assuming "us" are Earthbound) breaks the reciprocity -- if only slightly -- that would be observed in Minkowski space.)
> Observers at a high cosmological redshift cannot watch our clocks at all.
This is true, but it doesn't change the fact that the "time dilation" described in the article is like the time dilation in special relativity, and is not like gravitational time dilation, with respect to what the article is talking about.
> there's no reason to think that the redshift we ascribe to them is the redshift they ascribe to our precursors.
Indeed, there is every reason not to think this. But that still doesn't change the fact that the "time dilation" due to cosmological redshift is like the time dilation in SR, not gravitational time dilation, with respect to what the article is talking about.
In the special relativistic setup in your final sentence, the spaceship occupants could in principle watch our clocks and observe that ours are ticking slowly, with the same redshift.
Observers at a high cosmological redshift cannot watch our clocks at all. They can only look at the even more distant past of what will become our clocks in billions of years, and there's no reason to think that the redshift we ascribe to them is the redshift they ascribe to our precursors.
(Indeed the gravitational redshift from the metric sourced by Earth (assuming "us" are Earthbound) breaks the reciprocity -- if only slightly -- that would be observed in Minkowski space.)