After being injected, one participant from each of the three groups wa

After being injected, one participant from each of the three groups was taken to an observation room where, they believed, they encountered someone that had had the same injection.

(A) they believed, they encountered someone that had had

(B) as they believed, they encountered someone who had had

(C) they believed that they encountered someone having had

(D) the participant believed they encountered someone who had

(E) the participant believed, he or she encountered someone who had had

Participant is singular, 'one of them' turns subject into singular: A,B and C out
The sentence is mentioning the time when the participants had those injection
the past form of past is past perfect, one happened before other ;
Hence had had is necessary, Eliminate D and C

Answer is E
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(A) they believed, they encountered someone that had had -> The partecipant is singular

(B) as they believed, they encountered someone who had had -> same reason A

(C) they believed that they encountered someone having had -> same reason A

(D) the participant believed they encountered someone who had -> "that had had"

(E) the participant believed, he or she encountered someone who had had -> Correct

After being injected, one participant from each of the three groups was taken to an observation room where, they believed, they encountered someone that had had the same injection.

(A) they believed, they encountered someone that had had Incorrect

meaning change - they refers to three groups, here each participant believe

(B) as they believed, they encountered someone who had had Incorrect

meaning change - they refers to three groups, here each participant believe

(C) they believed that they encountered someone having had Incorrect

meaning change - they refers to three groups, here each participant believe

(D) the participant believed they encountered someone who had Incorrect

pronoun error - the participant singular , they plural

(E) the participant believed, he or she encountered someone who had had Correct
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Is it just me or does it seem like the sentence is a bit confusing. "one participant from each group" means more than one individual (i.e. plural) so I am not quite following the exclusion of the plural choices involving "they" above.
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I have the same question. One participant from each of the 3 groups means 3 people, hence 'they' should be applicable.

I think the subject remains that one person throughout the sentence. It doesn't shift to multiple people even though there are 3 people in the room now.