Is it true that rainforest are responsible for most global oxygen turnover?

The answer is that they do.

Terrestrial plant account for 52% of the oxygen production, and aquatic only 48%.

Of that 52%, almost all of it is by rain forests. Agricultural crops produce some oxygen, but end up as a wash because of all the use of oxygen in the planting, cultivation, harvesting, processing, and distribution.

Rain forests are the single most important contribution to global oxygen production.