Is the iPhone's "found this contact info in.." reliable?
Reliability is not a binary, black/white property. You'll find cases where this feature doesn't work at all, suggesting the wrong thing - and you'll find cases where it does work, suggesting the right thing.

I don't have any statistics on exactly what the hit/miss frequency is. I doubt if anyone does - perhaps Apple has some statistics. However, in my own experience it works fairly well. It can be a convenience that a phone call from an unknown number is instantly matched with the contact details from an email, you've received yesterday for example.

The matching is done by the Spotlight functionality on the phone. Basically an index is created of for example your emails inside Mail.app. When for example a call comes in, and the number is unknown, then iOS will automatically search your Spotlight index for emails to find e-mails mentioning that phone number. The contact information will then be derived from the mail using proprietary heuristics.

The implementation of this feature is entirely on the phone. It does not require a cloud service, nor does it send your data off for processing somewhere on the internet. So your question about "big brother" is that no "big brother" is involved.

If you want, you can disable this feature from Settings > Contacts > Siri &amp; Search > Find Contacts in Other Apps.