Amazon? Lungs of the world? Sinking feeling?

I got into this debate, related to Global Warming, on the "Amazon is sometimes referred to as the Lungs of the world."
Here's a very readable discussion in Newsweek on how much oxygen comes from the Amazon: https://www.newsweek.com/how-much-oxygen-amazon-rain-forest-1456274
Much like Global Freezing, I don't know that I have ever heard/seen an actual scientist say this, but the Lungs of the World is still a pretty well circulated myth. Some times it says 20% of the oxygen in the world is produced by the Amazon Rain Forest. Actually, this is probably true, however the rainforest consumes most of the oxygen it produces. Plants (decomposition) consume it, animals in the forest, not so much so. Oxygen in the atmosphere is about 21% (20.95%, actually). And that's not going to change much, even if the Amazon was burned to the ground... Carbon Dioxide (CO2) on the other hand, that's not so pretty.
There's massive amounts of carbon stored in the trees and peat. That would all get moved from a stored state into the active environment (air and ocean). Same as chopping down 500 year-old native trees and burning them without replanting the same. Same as digging up coal that took 500m years to form and burning it (except that there's no way to return the coal in coal back to the sync from whence it came).
So, when the amazon is converted to grassland and ranching, the original carbon store is released into the atmosphere and the ability to store carbon (sync) is broken. Yes, grass is green, but it does a horrible job related to carbon sequestering compared to trees. Plus cows have a habit of belching and farting that releases a wicked amount of methane (32 to 64 times as potent a greenhouse gas as CO2).
Of course, there horrific impact on the environment. You could easily call this a crime against humanity and against the environment when native populations are killed and displaced and the rainforest with all it inhabitants of plants and animals are killed and destroyed forever.
National Geographic talks about the same issue, but follows on to discuss biodiversity: Why the Amazon doesn’t really produce 20% of the world’s oxygen: Of the many important reasons to worry about the thousands of fires raging in the world’s largest rainforest, oxygen supply is not one of them.