This is widely believed, and of course Ukrainians prefer no article, and I'm happy to accede to their preferences, just as with their preferred transliteration of Kyiv.
But the theory that this has any impact on how English speakers view sovereignty is also completely bunk. While English does indeed use "the" for some geographical regions and features (but not universally; English rarely is so simple), in international contexts and sub-regions, that's swamped by more salient examples. Look right there at your use of "the" USSR. We don't talk about "the Scotland" and "the England" as part of "United Kingdom", nor about "the California" and "the Texas" as purely internal regions of "United States", but quite the reverse, reserving. In keeping with groups of smaller units, there's also the EU. There are also many examples of full names that include qualifying adjectives that take "the" -- i.e. the Central African Republic, the Dominican Republic, and historically the Czech Republic (now Czechia is preferred, of course).
There are also, of course, countries named after geographical features that traditionally do have the definite article, but this is rarely taken as a slight against their sovereignty or an accusation that they're not a real country: the Ivory Coast, The Netherlands, many, many island nations.
And why would the Russians even think to use articles to make this distinction? Neither language even has a definite article! There is a history of using different prepositions in these languages ("in" vs "on", roughly) which does have this suggestion, but it really doesn't parallel English usage of articles.