Your question "Is this true to some extent" (that oaks will die off from root damage)

Second part: "Yes but the implication here is that oaks are in particular much more susceptible to damage from roots than other trees."

My answers: "Oaks are way more susceptible to pests and diseases, because of this 1/3 are near extinction and another 1/3 is under preservation consideration." and "Roots are the life blood of a tree, damage to that makes them particularly vulnerable" (paraphrasing)

To absolutely and clearly answer your question using the answers I have already provided: Yes, Oaks are more likely to die from minor damage to the roots than other trees because they are a lot more susceptible to pests and diseases. So vunerable in fact that 2/3rds of all species are at least in consideration for conservation. So minor damage to the roots is, again, much more likely to be fatal to an oak versus other trees.

If that does not explicitly answer your above questions than I do not think it's possible to answer your questions with the way you've provided them.