The qualities of remembered experiences are often used to inform “reality monitoring” judgments, our ability to distinguish real and imagined events. Previous experiments have tended to investigate only whether reality monitoring decisions are accurate or not, providing little insight into the extent to which reality monitoring may be affected by qualities of the underlying mnemonic representations. We used a continuous-response memory precision task to measure the quality of remembered experiences that underlie two different types of reality monitoring decisions: self/experimenter decisions that distinguish actions performed by participants and the experimenter and imagined/perceived decisions that distinguish imagined and perceived experiences. The data revealed memory precision to be associated with higher accuracy in both self/experimenter and imagined/perceived reality monitoring decisions, with lower precision linked with a tendency to misattribute self-generated experiences to external sources. We then sought to investigate the possible neurocognitive basis of these observed associations by applying brain stimulation to a region that has been implicated in precise recollection of personal events, the left angular gyrus. Stimulation of angular gyrus selectively reduced the association between memory precision and self-referential reality monitoring decisions, relative to control site stimulation. The angular gyrus may, therefore, be important for the mnemonic processes involved in representing remembered experiences that give rise to a sense of self-agency, a key component of “autonoetic consciousness” that characterizes episodic memory.