Weird Wikipedia Section on Oxidizing Behavior of Nitric and Sulfuric Acids
It is chemistry that is being weird not Wikipedia

The trouble with simple explanations of oxidising acids is that there is no simple explanation that covers all the cases. The specific reactions leading to oxidation are complicated and have a variety of different mechanisms. 

So copper in sulphuric acid can be oxidised by a reaction that involves SO2 production. That has a completely different mechanism to the reaction with nitric acid and a different concentration dependence.

And, given the variety of reactions, the need to have protonated molecules of the acid is not a good generalisation: it depends on the specific reaction that is happening. 

The oxidising reactions depend on the substrate being oxidised as well as the acid. Which mechanism will dominate isn't easy to determine without trying the reaction. So don't trust simple generalisations.