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This is pretty reasonable advice. There was a time when linked-lists didn't have such a massive performance disadvantage compared with more contiguous data structures, but that time has passed and I'm not sure that the programming community is fully aware of it (certainly you wouldn't be explicitly told it in most CS programs). Memory efficiency is also often terrible on 64-bit machines, especially for doubly-linked lists.

Sometimes they're the right data structure, but I've definitely come across programmers who want to use a linked list for everything, even in code where performance is important.

Edit: the general advice that you should avoid linked lists for performance reason is good. The idea that you should never use them I just took as additional trolling for page views.