This is the 1505th most frequent Russian word.
отказались
"Отказались" means "refused" or "declined."
The word 'отказались' is used here to express declining or rejecting an offer, in this case, a proposal.
Они отказались от предложения.
They declined the offer.
In this sentence, 'отказались' indicates the refusal to accept or believe rumors.
Мы отказались верить слухам.
We refused to believe the rumors.
The word 'отказались' is employed to show withdrawal or renouncing participation in an activity, namely the project.