I find that believable, but we're talking about carbon, not oxygen.
Forests do sequester carbon for a period, although most of it is released again in fires and decomposition (chemically just a slow fire.)
But the point is that a forest locks up a lot of carbon compared to cleared grazing or cropland.
According to the documentary "One Strange Rock", which I admit I have not fact checked, your statement is absolutely false. The documentary claims 100% of the oxygen produced by the Amazon rain forest is used up by the animals that live in it.
EDIT:
Also this PBS article backups the claim. https://www.pbs.org/newshour/science/no-the-amazon-fires-won...
"Forest plants produce lots of oxygen, and forest microbes consume a lot of oxygen. As a result, net production of oxygen by forests – and indeed, all land plants – is very close to zero."