Not automatic removal
Google may show a known URL without crawling it. Crawl blocking is not index removal.
FinFly Explains / IT
robots.txt controls crawling
It tells compliant crawlers which URLs they may access.
Privacy is separate
Private areas need access control. Disallow is public and cannot stop non-compliant clients.
FinFly practice
Check image and stylesheet access. A crawler must be able to see a noindex directive to process it.
Method
Primary sources
The explainer is checked against these institutional and industry sources. Links open the original material.