You absolutely, 100% can handle billing completely outside of Apple's infrastructure and have your app be a "Reader app," to use Apple's term for such apps. Apple just posted a document[0] that lists Amazon Kindle, Netflix, Audible, and Spotify as examples of this.
You seem very confident about your understanding of things, but you seem to have misidentified the exact cause of your rejection.
We are writing to let you know the results of your appeal for your app, XXX.
The App Review Board evaluated your app and determined that the original rejection feedback is valid. Your app does not comply with:
Guideline 3.1.1 - Business - Payments - In-App Purchase
We continue to find that your app offers a subscription with a mechanism other than the in-app purchase API.
While we understand that the app reads data, it does not fall into any of the categories listed in guideline 3.1.3 for reader apps:
3.1.3(a) “Reader” Apps: Apps may allow a user to access previously purchased content or content subscriptions (specifically: magazines, newspapers, books, audio, music, video, access to professional databases, VoIP, cloud storage, and approved services such as classroom management apps), provided that you agree not to directly or indirectly target iOS users to use a purchasing method other than in-app purchase, and your general communications about other purchasing methods are not designed to discourage use of in-app purchase
We hope you will consider making the necessary changes to be in compliance with the App Store Review Guidelines and will resubmit your revised binary.
Best regards,
XXX
App Review Board
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So unless you are in one of those listed categories, it does not work. Don't know why we can't be considered to be a professional database tho.
