More importantly as the planet's "lungs" the Amazon filters a great quantity of carbon dioxide from the air.
Does the Amazon provide 20% of our oxygen?
is equivalent to
Does the Amazon remove 20% of our waste carbon dioxide?
The main part of the "lungs" of the planet is the phytoplankton in the sea.
Quote: "The Amazon Basin is critical to help mitigate climate change due to its trees absorbing around a quarter of the CO2 released each year from the burning of fossil fuels."
The specific quote is talking about trees in the rainforest, not the rainforest itself. The rainforest is an ecological system that also produces CO2 (mainly through microbes breaking down wood) and you can't ignore the rest of the system.
Which is not to say that the Amazon doesn't play a significant in the global environment and weather systems.