Recent developments in neural language models (LMs) have raised concerns about their potential misuse for automatically spreading misinformation. In light of these concerns, several studies have proposed to detect machine-generated fake news by capturing their stylistic differences from human-written text. These approaches, broadly termed stylometry, have found success in source attribution and misinformation detection in human-written texts. However, in this work, we show that stylometry is limited against machine-generated misinformation. While humans speak differently when trying to deceive, LMs generate stylistically consistent text, regardless of underlying motive. Thus, though stylometry can successfully prevent impersonation by identifying text provenance, it fails to distinguish legitimate LM applications from those that introduce false information. We create two benchmarks demonstrating the stylistic similarity between malicious and legitimate uses of LMs, employed in auto-completion and editing-assistance settings. Our findings highlight the need for non-stylometry approaches in detecting machine-generated misinformation, and open up the discussion on the desired evaluation benchmarks.