In the case of Millikan's experiment, we are considering something in the order of a dozen repetitions. With these temperature measurements, there are thousands

In the case of Millikan's experiment, we are considering something in the order of a dozen repetitions. With these temperature measurements, there are thousands. This alone makes it rather implausible that we have a false signal that is the consequence of an initial error. Furthermore, unlike with the charge of the electron, there is no strong reason to believe the value is a constant. In fact, it is known to be variable, and that variability has been recognized as diagnostic (which is why we have a lot of measurements.) As others have pointed out, the authors have considered, in detail, several conceivable sources of systematic error. We probably should not approach studies with the expectation that the people performing them are naive.