Suppose that $P \not= NP$. Then my understanding is not all instances of NP-complete problems can be solved in polynomial time. That is for every NP-complete problem, there are a colleciton of instances of that problem where the solution (correct certificate) cannot be determined in polynomial time (I do not mean that there is no algorithm that solves it in polynomial time, like the algorithm that just hard codes the instance and knows the correct certificate).
Is what I have said here correct? If not, what exactly does "worst case complexity" when $P \not= NP$ mean, if it does not mean there are instances of NP-complete problems that no algorithm can find a solution (correct certificate to) in polynomial time?