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Policy testing is an important means for quality assurance of access control policies. Experimental studies on the testing methods of XACML policies have shown their varying levels of effectiveness. However, there is a lack of explanation for why they are unable to detect certain types of faults. It is unclear what is essential to the fault detection capability. To address this issue, we propose a theory on policy testing by formalizing the fault detection conditions with respect to a comprehensive fault model of XACML policies. The detection condition of a policy fault, composed of the reachability, necessity, and propagation constraints, is sufficient and necessary for revealing the fault. The formalized fault detection conditions can qualify the inherent strengths and limitations of testing methods. We have applied the formalization to the qualitative evaluations of five testing methods for the current version of the XACML standard. The results show that, for each method, there are certain types of faults that can always or never be revealed, while the detection of other faults may depend on the particular policy structure.