"Privacy-first" is easy to put on an App Store listing — verifying it takes a bit more than reading the tagline.
Check the App Store's own privacy label
Apple requires every app to disclose what data types it collects and whether they're linked to your identity — a document scanner claiming full privacy should show minimal or no data collection categories, not just a marketing claim on its listing page.
Test core features in airplane mode
If scanning, OCR, or export stop working without internet, the app is very likely sending data to a server for that feature — genuinely on-device features keep working with no connection at all.
Read what the privacy policy actually says
Look specifically for language about whether document content is transmitted, and to whom — vague language about "industry-standard security" for uploaded data is a different (weaker) claim than "content never leaves your device."
Does requiring an account automatically mean an app isn't private?
Not automatically, but it does mean some data — at minimum an identifier tied to you — is necessarily stored somewhere outside your device, which is a different privacy posture than a fully anonymous, accountless app.