Du hast recht. Except in certain cases such as "selbstverständlich." Endlich = finally Wirklich=really etc. Aber selbstverständlich=? This one is an adjective, whereas "-ly" is a standard adverb ending.
Why would "kürzlich nicht" be correct, but not "plötzlich nicht"? They look as if they have the identical form, just different adjectives. (There were three selections offered, and the task was to select ALL that were correct.)