Basic action for every data structure O(1)
What was meant is that every data structure is designed to do something really well, e.g:


For an array, lookup by index is O(1)
For a linked list, insertion at the head is O(1)
For a heap, finding the smallest element is O(1)


... and so on. This doesn't mean that the operation that is O(1) for one data structure wouldn't have much worse complexity for some other data structure.