Ok, so I asked this question on the theoretical CStheoretical CS stack exchange website.
Louis has given what I think is the most suitable answer to this question:
Your implementation of linked lists also needs to be able to access memory non-sequentially for the pointer operations that splice in the new value.
That is, when I am inserting a new node at an arbitrary location in the linked list, I am assuming I have random access. Else, I would have to shift all the subsequent nodes ahead in memory before adding the new one.