And of course I'm not claiming that the word "ukraina" was used to refer to what today is the country Ukraine back in 1200s - that would be ridiculous, for exactly the reasons you cite above. No, my point rather is that the word "ukraina" - "оукраина" - is attested in documents from that period to refer to areas that they (the Kievan Rus state) considered borderlands, and has fairly obvious and transparent etymology of "u+kraina", both parts of which are also attested in written sources.. It is solely about the etymological origin of the word - that, yes, it does in fact mean "borderlands" historically - not about the origin of the name "Ukraine" for the country. That came much later.

As for the latter, it shows up first somewhere circa 1600s, and it first appears in Polish sources (as self-designation of people inhabiting the territory). At that point, the entire Western and Central Ukraine was a part of the Polish-Lithuanian Commonwealth - and for them, it was definitely "borderlands" in all senses. Geographically it was the easternmost territory of the state. Culturally it was significantly different from Polish heartland - language, religion etc - and further east and south there were culturally alien Turkic (Tatar) tribes. Militarily, it was a buffer zone between the Commonwealth and the Tatars, and to some extent with Russia, with constant low-key hostilities.

https://en.wikipedia.org/wiki/Polish%E2%80%93Lithuanian_Comm...

It's exactly the kind of area that would be called e.g. "the Mark" in German-speaking parts of Europe. Indeed, when the revived Polish state later occupied large parts of Western Ukraine after WW1, they referred to it as "kresy wschodnie" in Polish, literally meaning "eastern borderlands" - old habits die hard.