"must have rendered" is not 'present perfect.' It is a modal form in the perfective (meaning 'before'), in this case 'before they decided.' It is a logical conclusion about what had happened before the utterance.
"I told him he must have made a mistake."
"I told him he had made a mistake."
"I told him he must come (the next day)."
which is about the same as:
"I told him he had to come (the next day)."