My reasoning?

Say that there exists a problem of the verify being O(n) and the finding being O(n²)

So then the increase in complexity results in O(n²)

Why shouldn't it in some other problem result in O(2ⁿ)?

Also, the problems are not equivalent. The verification problem is a problem related to the output of the solver. This is not equivalent

Say, perhaps, the sub sum problem. The verification is NP if we ask if the sum of the values' factorials are 0

So then, we can look at data access. Again, the sub sum problem. The issue of verification is taking the interrelated value of the whole set. The verification has nothing to do with subsets. The finding issue has to search all the subsets

Besides, let us assume it is a sub div problem. The verification need only divide all the elements in order. The problem is whether the division of all the elements is equal to one of the elements of the set. Meanwhile, due to x/y!=y/x, the search for such a set must include more of the permutations of the set. This would require an NP algorithm and thus a verification problem for such a must be NP problem could be made P