Tranfer/transit via Schengen area with 2 separate tickets and no visa [duplicate]

Yes, it is true. The first airline would likely not let you board the flight if you do not have the right documentation for entering Schengen.

They're doing that to protect themselves. If somehow you can't get on the second flight -- which may happen for reasons the first airline has no control over, such as the second airline canceling the flight, or denying you boarding due to overbooking or whatever -- then you'd be stuck at the Schengen airport, and the first airline would be in hot water with the authorities for transporting someone who doesn't have the right papers to enter the country they flew him to.

Naturally they don't want to take that risk for free. The price you need to pay for insurance against that situation is that fares that allow combination into interlined itineraries may be more expensive that one-airline-only offers.

(By the way, you shouldn't assume that just because you can't buy a combined ticket on the airline's own website or at an online travel agency, it can't be bought at all. If you go to an actual human-staffed travel agent, they often have the means to sell interlined tickets that can't be specified on websites. That may not be as cheap as the no-connection combination you've found for yourself, since the travel agent wants to be paid for their services. But it may well be cheaper than any actual connection you can book online).

When buying a single ticket you are entering a contract with airline with their obligation being transferring you from Brazil to Turkey. Nowhere does it say they are obligated to carry you via Portugal. They could, for example, route you through Panama City instead of Lisbon. That you most likely will end up in Lisbon is more of a side effect and the authorities kind of let it slide. They weighted the various costs of people trying to dodge the visa rules via doing this sort of hidden city ticketing vs the cost of issuing many more transit visas (plus the associated costs of less people using their airports) and decided to let it slide.

If you buy two tickets, the entire thing is very different. Now you are 100% to end up in Lisbon. They do not let this one slide. Such "flight hacking" is much rarer and it's much harder to police -- what if your second ticket is a rouse, a refundable ticket that you will cancel the moment you are checked into the first plane? So, the powers that be simply decided the cost analysis is not favorable for this one.

Edit: to better understand what this answer is about, it's a possible explanation on how this situation came to be. It's pointless to argue with us, random strangers on the Internet or the airline check in agents or even the border guard. There is legislation, it is what it is, it doesn't matter whether it is logical or not. Dura lex, sed lex: the law is harsh but it is the law. If you want to argue, you'd need to argue in the European Parliament (or rather find an MP who would argue for this change).