Is the iPhone's "found this contact info in.." reliable? Got an SMS from a new contact I know, saying simply "hi it's Jane and peter"

I don't have any address book entry existing for this person but the phone suggested "maybe:Jane" - ok, I can see that conclusion

However, tapping the banner at the top of the message it said "contact info for Jane.. blah blah cellphone number 123 456 789.. found in Mail"

And then it showed a mail from my account manager at my insurance broker confirming a policy detail - entirely unrelated to this person, the trailing phone number digits are different, all names are different, they'll never have met or interacted etc.  I can't find anything they have in common - just wondered if it's reliable, how it matches, what data big brother is linking up to offer this assist etc?
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.