You don't need to store CO2. You need to store the carbon somewhere and get some O2 for free. There's about 2.5g of oxygen per 1g of carbon in carbon dioxide,

You don't need to store CO2. You need to store the carbon somewhere and get some O2 for free. There's about 2.5g of oxygen per 1g of carbon in carbon dioxide, and carbon takes the lion's share of hydrocarbons' mass, so I wouldn't be surprised if just the cork itself would burn to twice its weight in CO2. Then you consider the growth of the tree itself over time. Oak is about 3-4x the density of cork, so I wouldn't be surprised if you got a few grams of wood per gram of cork. That 70x multiplier is enormous and probably overinflated, but these are just two factors I could think of in a couple of minutes, so I can easily see how a tree, over its lifetime, might sink 10-20 tonnes of carbon per 1 tonne of cork produced.