Hi James,
I see it as follows.
With the quote above, Jesus gives you the basic interpretation of the law - the Torah. The commandments you mentioned fall under what you call the Golden Rule because Christ said so.
The reason why we often understand them differently is that, on the one hand, we do not know the context in which they are embedded. On the other hand, they are translated improperly.
The English word slave, for example, evokes completely different associations in us than the original text means. We see the deprived Roman slave before us. But that is not what the Hebrew word eved means.
But that is a topic for a future article.