Your agreement is not required. Science does not do negative proof. It provides evidence, and you make up your own mind - big difference.
I’d like to think that I’m not being dogmatic.
No offense intended here - but you sound that dogmatic. If you actually aren't, then somewhere between your brain and my brain there's a disconnect. Not unusual, in the text-only medium.
You say: “You might do a study and show that correlation between astrological prediction and actual outcome is at or below what you'd expect from random chance.” It has been done. Astrologers work on inaccurate and outdated star charts and cannot even agree amongst themselves.
Yes. That evidence would, to most rational people, indicate that it is highly improbable that astrology works. It is the basis for a belief, but it is not proof that astrology cannot ever work.
For example, the jury is still out on whether our universe is deterministic - some forms of string theory still allow that. If it turns out to be true, then there's no such thing as "unrelated events", as all events would be related to the one event that started the Universe, and many forms of "divination" become possible. This would not be "spooky action at a distance", but simple correlation of events, a fundamental interconnectedness of all things. Not that this would matter much, as in a deterministic universe you cannot change the future, so knowing it would be kind of moot. But the point still stands.
Dude, I'm a physicist. I am a skeptic, and I don't believe in astrology. However, as a scientist, I know the bounds of what I can and cannot say - I can say I don't believe that it works, but I cannot say that it cannot work.