Well, yes, if you're talking about a recorded <i>monologue</i>, as we saw in the video. On the other hand, being able to recall and use appropriate native proverbs/idioms in an unscripted, spontaneous, multi-topic conversation with a native speaker would demonstrate a higher level of fluency in the target language.
True, the sparrow probably wasn't a very good example -- I doubt any ESL teacher would include "sparrow" on a vocabulary list for students below the advanced level. (Whereas words like "chicken", "pigeon", and "parrot" might be introduced even in a beginning class, although after the generic term "bird".)As for the воробей, I would answer "it's a small bird" in English, because I don't know one wild bird from another. Does that mean I'm not fluent in English?