Automated fact-checking is a needed technology to curtail the spread of online misinformation. One current framework for such solutions proposes to verify claims by retrieving supporting or refuting evidence from related textual sources. However, the realistic use cases for fact-checkers will require verifying claims against evidence sources that could be affected by the same misinformation. Furthermore, the development of modern NLP tools that can produce coherent, fabricated content would allow malicious actors to systematically generate adversarial disinformation for fact-checkers. In this work, we explore the sensitivity of automated fact-checkers to synthetic adversarial evidence in two simulated settings: ADVERSARIAL ADDITION, where we fabricate documents and add them to the evidence repository available to the fact-checking system, and ADVERSARIAL MODIFICATION, where existing evidence source documents in the repository are automatically altered. Our study across multiple models on three benchmarks demonstrates that these systems suffer significant performance drops against these attacks. Finally, we discuss the growing threat of modern NLG systems as generators of disinformation in the context of the challenges they pose to automated fact-checkers.