That quote has some validity yes. Luther and Calvin especially were moved by Augustine and much of their theology was shaped by him. One thing to keep in mind is that how one viewed a teaching 1000 years after it is taught may not be the same as what the teacher had originally intended it to mean. But I don't think that Luther, in particular, and the Reformers in general, are tied to the teachings of Augustine in such a way that they fall if he falls. I have Luther's commentary on Romans. Here is what he says of Romans 79-10 and Augustine's position on it,

There are some, and among them Saint Augustine, who denied that the Apostle speaks of his own person, and indeed of himself of being spiritual and not as carnal. But the whole passage shows very clearly a strong hatred against the flesh and a sincere love for the law and all that is good. No carnal man ever does this. He rather hates the Law and follws his flesh and evil lusts. The spiritual man fights against his flesh and deplores that he cannot do (as a new man) he desires to do.*

Luther here does not comply with Augustine's interpretation. So I don't think that we can say that his arguments for predestination, unconditional election, and all his theology rises and falls with Augustine. I would say that of all of the Reformers because their theology does not completely cohere together within themselves.




*Luther, Martin, trans. Mueller, Commentary on Romans; Grand Rpaids, MI: Kregel Publications, 1974; 112.