Fast-gated avalanche photodiodes (APDs) are the most commonly used single photon detectors for high-bit-rate quantum key distribution (QKD). Their robustness against external attacks is crucial to the overall security of a QKD system, or even an entire QKD network. We investigate the behavior of a gigahertz-gated, self-differencing (In,Ga)As APD under strong illumination, a tactic Eve often uses to bring detectors under her control. Our experiment and modeling reveal that the negative feedback by the photocurrent safeguards the detector from being blinded through reducing its avalanche probability and/or strengthening the capacitive response. Based on this finding, we propose a set of best-practice criteria for designing and operating fast-gated APD detectors to ensure their practical security in QKD.