There's a difference between the German 'können' and the English modal verb 'can - be able to'. In English you always have to use the modal with a main verb, unless you use it in a short answer or statement (yes, we can), where the main verb is implied. Of course, it's similar in German, but the use of 'können' without a main verb it taken further than in English, it can even have an object: Kannst du Deutsch? Ich kann Englisch und Französisch. The implied verbs may be sprechen, verstehen, lesen, schreiben; 'können' here is used like 'beherrschen' (to master). Similarly in your example the implied main verbs could be 'sprechen, übersetzen, verstehen'; because you have learned these words you can say them, use them, understand them. In German we say: Wenn du es gelernt hast, kannst du es. I might ask someone if they have learned a poem or a list of words: Kannst du es? Kannst du sie? i.e. Can you recite it, can you use them?
Your interpretation is not wrong, it just shows a problem of the English verb 'know', which can be used for German 'kennen', 'wissen' and 'können' (in the above sense).
'Du kennst nur wenige Worte' - you are acquainted with just a few words. 'Du kannst nur wenige Worte' - you know how to say or use them, you understand them because you have learned them (Du kannst sie).
Think of this problem from the point of view of a German learner of English, you can guess what mistakes they might make :-)