Another thing to consider is that Klingons may have studied Earth literature in a way that Earthlings hadn't looked at Klingons' and using this to subtly mock Kirk with, since Kirk (and more of the bridge crew than we'd ever considered before) loved Shakespeare. This makes Chang even more fascinating, given how he first boasts "To be or not to be!" with all the other Klingons bursting out loud in laughter, before it quickly becomes serious about the fate of their people. (or did I reverse the two moments? Am rewatching today after buying popcorn and coffee latte...) Chang later spouts out the line during his attack on Enterprise as the torpedo is heading toward his ship, so there is some certainty that - regardless of what piqued their interest - Chang and others relished the style and ideas Shakespeare had... As Data might inquire, "Is imitation not the most sincere form of flattery?"
Also, sausage omelets are cool.
Or ST6 was just parodying Chekov by saying Klingons did it all first as a weird backhanded joke. Which seems less likely, but as there are invariably a statistical quantity of people love the taste of coffee with spirulina flavoring then anything is truly possible...
