Well, not quite, the decision table is great as a way of specifying the functionality, and also for guiding the test specification, but saying there are only five tests needed only leads you to tests that the system works as specified for correct inputs, and not to tests that the system doesn’t do the wrong thing for incorrect inputs.
This means that, in the example, you need to be sure that the unauthorized user doesn’t get issued the chemical for all possible combinations of the other three conditions.