A few weeks ago a friend and I were talking exclusively through WhatsApp about a trip to London(in Portuguese with our very unusual jargon), I didn't do any search for anything related it was all within our conversation, a couple days later Facebook had a post on my timeline saying: "heading to London? Check what your friends did there".
I don't remember reading anywhere that WhatsApp reads your conversations for ads, but it was clear to me that's where they got the information, it was spooky at first.
Speaking of which, I had a similarly creepy moment just yesterday. I was watching an episode of the Simpsons, and wanted to Google the Bart blackboard gag in the intro because I didn't get it. Just I type the first word and it immediately suggested the rest. Very creepy because I wasn't watching through any Google service (on an Android phone though).
The late 1970's was probably the last time anybody truly understood 100% of what was going on in any system.
The bottom line is that you have to trust some people. I totally understand those that don't trust Google. I happen to trust them today.
- no scanning emails
Are different things
In this case it is google's code running on google's computers.
Which is mostly based on Free Software, starting with GNU/Linux. The Affero General Public License is intended to disallow this loophole of "it is only running on our servers, hence we are technically not distributing it, so we do not have to release the code": https://www.gnu.org/licenses/agpl-3.0.html