When the authors wanted a roll to be a test, they use that term. Analytical Mind applies to "logic based tests" not logic based rolls. The Drain sections (two of them) say to make a roll, not a test. The designers wind up using a lot more words and wasting ink and paper to present it the way they did. I believe the intent was that Analytical Mind should not apply to Drain, and the technical reading does not permit it.
If Analytic Mind were to apply to Drain, it would be a cheap Edge machine. Many will be recasting buffs at the start of the day anyway, so those casters have the opportunity to pound out massive Edge that non-casters cannot. Allowing it to apply creates significant unfairness, or the technical term, imbalance.