Border control between Zurich/Switzerland- Ibiza/Spain?

If acquaintance has a Mexican Passport like you do then s/he is full of it.

Here are the requirements from the official government site and you only need visa for 90 days or more

https://www.sem.admin.ch/sem/en/home/publiservice/weisungen-kreisschreiben/visa/liste1_staatsangehoerigkeit/m.htmll

Just to be clear, the Schengen Treaty removed routine border checks, but gives individual countries the right to perform targeted checks.

the Schengen Treaty removed routine border checks, but gives individual countries the right to perform targeted checks.

And I believe that if a country declares a state of emergency (like France has done), they can have routine checks at specific borders.

In other words, it would be good to have your passport easily acceptable to you while traveling between countries.

At these troubled times, even for an internal flight you are likely to be requested to present ID multiple times: at check-in, at security control, at boarding. On a Schengen flight you skip the immigration stage, but you may still be requested to identify yourself.

Going from Zurich to Ibiza you will not be subject to immigration control, but in theory you could be subject to customs control as Switzerland is not part of EU - your luggage tags will not have green bands identifying luggage flying within EU and so being exempt from custom checks.

The airline always requires ID, and that would normally be your passport which you would show at check-in and again before you board the plane. This is not border control, this is company or airport staff checking that your name matches the ticket.
Landing at Ibiza, as lachera says, from Zürich that is ex-EU, so you go through green "nothing to declare". If your friend went through blue EU exit with non-EU bags they would have been pulled over, or maybe they got the 1-in-100 random check in nothing-to-declare.
Customs can ask for ID (as can any policeman in the street), but you are only stamped in and stamped out when you enter or leave the Schengen Area.

A few hours ago I crossed from Switzerland to Germany and back again. Crossing into Germany there were 3 "Bundespolizei" (Federal Police) looking in the train window, presumably for illegal immigrants, but they didn't get on. Coming back, nothing.

Yesterday someone on an RS forum said that recently when he flew from the US to Marseilles via Amsterdam he went through immigration in Amsterdam (as expected) and then again when he got off in Marseilles. I'm now curious what will happen next week when I fly Boston to Amsterdam to Lyon.

Yeah but France of course is still under a state of emergency..
We were there flying in from Italy recently and went through a light passport control check.
The line went fast.

As several people have posted above, being asked to show your passport (often required for ID, like when boarding a plane) is not the same as immigration/passport control. However, I've often seen people think they are the same. So, maybe your acquaintance mixed them up.

The Schengen Treaty only removed systematic border controls. It did not remove all checks. Immigration officers can still conduct spot checks whenever and wherever they see need for that. It's not unusual for them, for example, to meet Schengen flights at the end of the jet bridge on arrival, asking everyone to show their IDs/passports. This happened to me on a recent flight from Athens to Warsaw (both Greece and Poland are Schengen countries). Last year I was on a bus travelling from Warsaw to Lithuania (both in Schengen) and immigration officers got on the bus some 100km before the border to check everyone's papers.

Also, if you not an EU/EEA citizen and fly some budget airlines like Ryanair, you need to have your documents checked as per their T&Cs
https://www.ryanair.com/gb/en/useful-info/help-centre/faq-overview/passports-and-visas/im-a-non-eu-eea-passenger-do-I-need-extra-travel-document-visa-check

I was the one who posted about AMS to MRS. My Schengen flight and a flight from Morocco were mingled, there was no spot anything, it was full immigration for everyone. There was no easy way for the French immigration guys to tell who came from which flight.