The comic does tread each word as a symbol, which is why it only claims 11 bits of search-space per word, which requires a dictionary of only 2048 words, and there are way more than 2048 words that are long enough that the fact that they're in a dictionary is the limiting factor. It's already accounted for in the search space estimate.
The claim of the comic hasn't been "debunked" because the claim isn't that you can use words to have a lot of characters in your password, it's that we've been focusing too much on getting the most search space out of each character when the thing we want to optimize is the total search space per password that a person can remember, and the word technique sacrifices a lot of character efficiency to result in better overall passwords.
Your hypothetical user isn't choosing between four words from in a 10k word dictionary and a 16 character password. The fully random 64-symbol password of equivalent memorability is probably quite a bit shorter than 16 characters. I wonder what research has been done on this; I'd put my money on the equivalently memorable password being closer to 6-8 characters.
It only takes nine words from a 10k dictionary to beat a 16 character (64 symbol space) password. It also only takes 21 lowercase letters to beat your "complex" 16 character password, and I know which one I'd prefer to actually have to type regularly. More symbols per element is only a benefit when it increases the ability of the user to actually use stronger passwords.