No, this is probably nonsense. Did the people telling you that cite any sources?
As you pointed out, any air trapped in the milk will quickly bubble out. If you wait a minute before feeding, there will be very little air left. As to vitamin A, it is true that it is broken down by oxygen, but I don't think a bit of extra air due to shaking will make much of a difference - after all, the milk powder has been exposed to air before, too.
In addition to that, all the official instructions for preparing milk from formula that I have seen tell you to shake the bottle, because it is the best way to make sure it is mixed evenly. Shaking is particularly important after heating, before checking the temperature, to make sure the milk is heated evenly.
For example, on the packaging of Hipp Combiotik (a popular German formula), it says (after telling you to add formula): "Close bottle, and shake vigorously".