It is not. Vocabulary is far from the binary of "you know this word or you don't". At a minimum, it is usually split into passive and active vocabulary, with passive being the words you understand when encountered, and active being the words you can use effectively. Wikipedia's entry is a pretty good overview.
It is more like an ability to recognize the word when it is used in context.
I got ~1/3 that is very generous estimate even for "recall" case (recognize), and it obviously false for the "generate" case (using in speech) where I guess my vocabulary is likely ~1/90 of all English words.
I think that picking the correct (or most correct, which is trickier) use of the word in context (out of, as you say, many options) might be a good way to test for receptive vocabulary.