Science

From my reading, you are correct, but their methodology for determining what type of coffee people drank was very limited and the authors know it. While they didn't see any of the issues they were tracking with normal filtered coffee, they did theorize a reason why instant may be a problem.

From the paper:

The health effects of instant coffee, which varied from other subtypes of coffee, might be caused by their different ingredients. The mineral lead in instant coffee was more abundant than that in other coffee types, and long-term consumption of instant coffee may result in excessive lead [41]. Additional substances added to commercial instant coffee, such as creamer and flavoring agents, might partially explain the negative effect [25,26].

Also:

Instant coffee consumption has been proven to be associated with obesity [44,45]. Compared to women who did not regularly drink coffee, those who drank instant coffee had a higher risk of developing breast cancer [46]. Instant coffee was regarded as a risk factor for Alzheimer’s disease and frailty in the elderly [47,48]. Instant coffee might have the effect of shortening telomere length, and might lead to the occurrence and development of diseases. Therefore, we emphasized the importance of coffee types and the consumption of instant coffee at an appropriate amount. More research needs to identify whether the ingredients in instant coffee results in shorter telomere length.

The paper then goes on to list the limitations they know to exist with their own research and suggest that more work be done.

I mean, dry instant coffee is concentrated, but the "end product" with water really shouldn't be any more than regular coffee.

But it's funny that they say "No causal relationship was found between filtered coffee intake and telomere length" when "coffee intake and instant coffee intake were negatively correlated with telomere length, which was equal to 0.12 year of age-related decrease in telomere length for each additional cup of coffee intake", which I took to mean that yes even "regular" coffee affects telomere length

The paper mentioned that lead theory which seems plausible, but I'd be willing to bet this is a classic "correlation != causation".

There's some evidence of socioeconomic stressors influencing telemere length and while I can't find any citations for it I would assume there's a decently strong correlation between instant coffee and poverty.