Recent years have seen a strong uptick in both the prevalence and real-world consequences of false information spread through online platforms. At the same time, encrypted messaging systems such as WhatsApp, Signal, and Telegram, are rapidly gaining popularity as users seek increased privacy in their digital lives. The challenge we address is how to combat the viral spread of misinformation without compromising privacy. Our FACTS system tracks user complaints on messages obliviously, only revealing the message's contents and originator once sufficiently many complaints have been lodged. Our system is private, meaning it does not reveal anything about the senders or contents of messages which have received few or no complaints; secure, meaning there is no way for a malicious user to evade the system or gain an outsized impact over the complaint system; and scalable, as we demonstrate excellent practical efficiency for up to millions of complaints per day. Our main technical contribution is a new collaborative counting Bloom filter, a simple construction with difficult probabilistic analysis, which may have independent interest as a privacy-preserving randomized count sketch data structure. Compared to prior work on message flagging and tracing in end-to-end encrypted messaging, our novel contribution is the addition of a high threshold of multiple complaints that are needed before a message is audited or flagged. We present and carefully analyze the probabilistic performance of our data structure, provide a precise security definition and proof, and then measure the accuracy and scalability of our scheme via experimentation.