I was offered a job in Brazil and wanted to make sure it was a good place for my kids so booked a flight the morning of the offer for a flight later that morning. I arrived at airport for my direct flight to Brazil, was issued boarding passes, took the flight but was refused entry upon arrival. The airline flew me back, but I think they shouldn't have even let me board since I now know Americans are not allowed to enter Brazil w/o tourist visa? I don't mind paying the cancellation fees but I feel the rest of the cost of the flight should be refunded? Am I correct?
The airline IS responsible for checking your visa before boarding, however that responsibility is for the good of the Brazilian government, NOT for the good of the passenger. By not correctly carrying out this check, the airline will likely be fined by the Brazilian government.
However, the airline has ZERO responsibility to the customer to check the visa. Visas are always the responsibility of the passenger. You failed to meet the requirements for entry into Brazil, and that is completely your fault.
Even if the airline had checked your visa, you would likely not be able to claim a refund of your ticket - unless it was a refundable ticket. Most airlines do not give refunds in the event that visa requirements are not met.
Currently, U.S. citizens require a visa to visit Brazil. There is an upcoming exemption for the Olympic Games, and there is also some talk about implementing a general visa waiver for U.S. tourists, but that hasn't happened yet.
The airline should have checked for your visa when you initially checked in for your flight; they have a system called Timatic which tells the airline what documents are necessary for a person of almost any nationality to enter a given country. In the case of your itinerary, it definitely makes clear that you needed a visa, and the airline should have denied you boarding.
What happens next is that the destination country will cause you to be returned to your point of origin at the airline's expense, and since the airline should have known you would be refused entry, Brazil may levy a significant fine against the airline.
Typically, airlines will apply the cost of any unused flight segments toward the cost of returning you to your point of origin. Finally, every airline I have ever heard of makes it explicit that the passenger is solely responsible for any travel documents they may need. So you are not likely to receive a refund of any sort.