Not sure what you mean by this. Higher false-positive rate compared to what? And given that bandits do not run for a predefined amount of time but converge at a rate proportional to the evidence (as opposed to your typical AB-test), a higher rate at which point in time?
Perhaps you mean that, because bandits typically run longer, there's a higher chance that they'll select an alternative that offers only a marginal improvement on the status quo whereas short experiments would just say "nah, no evidence that one is better than the other" and thereby get rid of a lot of noise?