Detective's Authority (探偵権限 Tantei Kengen ) is a genre convention necessary for compliance with Knox's 8th (or Van Dine's 1st.) No matter how expansive or restricted this authority is granted in the story (or by the Game Master), the detective must not be hindered in discovery of clues necessary to solution. The detective's inspection is to be considered exhaustive to the extent that it obviates any Devil's Proof; clues not yielded to the detective also eliminates any resolution those clues would have proven.
Because this was never disclosed to Battler he never knew how to take advantage of it, or when he actually was making use of it. Though Beatrice neglected to inform him, she deferred to it (inconsistently) by yielding facts of the case in Red Truths. Only when Erika arrived armed with the knowledge from Bernkastel and exploited it to its limits was Battler able to learn of it and how it functions.
After invoking Detective's Authority, Erika was able to simply have her personal observations rubber-stamped in Red Truth. In Dawn of the Golden Witch she refrained from invoking it, but her strategy to compensate was functionally equivalent: she could demand clarifications in Red Truth, and would be entitled to the ones that support or disprove her hypotheses. As per the 8th, she would require the same clues to form deductions with.