Not confused, though you are correct that we already know that at least some NP cannot be solved in linear time given that NP is a superset of P. I should have

Not confused, though you are correct that we already know that at least some NP cannot be solved in linear time given that NP is a superset of P. I should have phrased things more narrowly. My point is simply to show that even linear-time problems may be computationally intractable.