Well, it comes down to the use of the zero-article versus the use of the definite article.
In simplest terms, the makes a definite reference, signifying you know which participants I am talking about.
Whether the has to apply to each individual participant, I am not sure.
It surely applies to participants plural, which to me seems to mean as a group.
It's been said before (notice the wonderful passive tense that does not require an actor!) that the before a plural count noun refers to all the "things" unless stated otherwise. This may be valid in some contexts but not all. For example, here it is a group of 20, in the other question it was to a relatively limited number of chemical companies.
It seems that for a larger group, not even all has to include each, at least not grammatically: (All) the residents of New York walk and talk fast seems to me a generalization even with all. While Each of the residents of New York walk and talk fast certainly seems like a reference to each individual citizen.
Thus, if you mean each, write each!
And there is a reason that the article refrained from using the. The zero-article certainly allows not much specific to be said about each individual participant in the referenced group. I am just not sure how much the has to attribute to (rather than just reference) each participant in the group. I think the use of the at least makes the statement possibly ambiguous. I wish I had a canonical answer.
The sentence can be rearraged to the following without a change in meaning, I think:
It is in (the) participants with depression that results showed a significant elevation of brain inflammation
What strikes me is is. Does this mean inside the participants (ie in their brains) or amongst or some other meaning of in?
I agree that it could be a matter of style. I think that the the refers to the group as an aggregate and that nothing definite can be said about each individual participant.