>Take measures based as though the complaints are made in good faith.
Which is to say, do more than just investigate. Take action as though the complaints are true, although not necessarily all the action you would take if you knew the complaint to be exactly factual.
You should always investigate, even if (to borrow your formatting)
you believe that
they believe that
their statements are false
and are making a bad faith accusation. It would still be correct to investigate if that was your belief. If you believed that the accusations were entirely factual, then perhaps the immediate step would be to fire someone. But if instead you simply believe that the person is accusing someone of something in good faith, something has already gone wrong and there is a problem. Even if no one did anything wrong.
To put it in terms that might be more familiar, every complaint is an incident and should involve a (blameless) postmortem that asks how the system failed such that someone felt the need to complain. And action should be taken in response. Sometimes, the system failed in such a way that it allowed a malicious actor to do a bad thing, and that malicious actor should be reprimanded, independent of the postmortem.
Believe the accuser when writing the postmortem, and begin incident response as soon as possible. Investigate fully before reprimanding a potential malicious actor.
It was badly worded, restated might be "as though the complaints are made in earnest though cannot be relied on as 100% factual". Which is to say, they should be taken seriously, and immediate action should be taken when possible, but insofar as all memories are fungible and witnesses unreliable, things should be verified when possible before certain measures are taken.
Which is to say, do more than just investigate. Take action as though the complaints are true, although not necessarily all the action you would take if you knew the complaint to be exactly factual.
You should always investigate, even if (to borrow your formatting)
you believe that they believe that their statements are false
and are making a bad faith accusation. It would still be correct to investigate if that was your belief. If you believed that the accusations were entirely factual, then perhaps the immediate step would be to fire someone. But if instead you simply believe that the person is accusing someone of something in good faith, something has already gone wrong and there is a problem. Even if no one did anything wrong.
To put it in terms that might be more familiar, every complaint is an incident and should involve a (blameless) postmortem that asks how the system failed such that someone felt the need to complain. And action should be taken in response. Sometimes, the system failed in such a way that it allowed a malicious actor to do a bad thing, and that malicious actor should be reprimanded, independent of the postmortem.
Believe the accuser when writing the postmortem, and begin incident response as soon as possible. Investigate fully before reprimanding a potential malicious actor.