So it's certainly plausible that the placebo effect of being involved in a study to prevent aging could in itself have an effect on telomere length, even without the hyperbaric oxygen.
I had a bone infection as a child that took several years to positively diagnose (it ended up being osteomyelitis). In an attempt to help my body fight off the infection, I was prescribed a couple hours a day in a HBO chamber.
HBO can be prescribed for infections of various kinds that are otherwise hard for the body to eliminate without assistance or straight antibiotics. This study aside, breathing pure oxygen for extended periods does wonders for the body's ability to repair itself.
The upside of that time was that bruises and mosquito bites healed practically instantaneously.
Placebo usually shows up in subjective measures, or where the brain can intercede to effect the outcome. There should be a control group, but I would not expect telomere length to be effected by placebo.
I agree, but a control group is important to avoid problems with other unknown unknown variables that are included in the non fancy part of the placebo effect.
For example:
Did the subjects change their diet? If you are enrolled in a medical study, perhaps you may decide not to eat junk food everyday because the doctors will screen you next week. (My grandma used to "cheat" at her medical exams, and eat only healthy food a few days before, so the cholesterol was low. In some cases, it may not be a conscious decision.)
Does the length change with the season? This should be a known effect, but to avoid problems just get a control group.
Is it possible that the technicians made an error counting the length of the telomeres? It is probably an automated test, so I guess no.
Is it possible that the technicians cherry pick the more healthy white cells in the second part of the study and that skew the results? I guess picking the cells to analyze is not automatic. Perhaps they changed the team. Perhaps the initial screen test if boring and they just pick the fist cells they see, and in the other test they are more motivated and try to pick a good one. (Some patients were excluded because they have too few white cells in the second test, it is weird.) A good way to avoid this problem is to have double blind studies, so the technicians can not involuntary skew the results.
https://www.tandfonline.com/doi/abs/10.1080/08870446.2019.17...
So it's certainly plausible that the placebo effect of being involved in a study to prevent aging could in itself have an effect on telomere length, even without the hyperbaric oxygen.