As a South Korean, this is a very interesting question. At the same time, a bit troublesome. Discarding all talks, the problem is: no English source, only Korean sources; and even those are limited. So please do tolerate some Korean characters and the short length of the reference list. Another problem is translation. I am not particulary familiar with how English-using scholars translates the Korean term; I'll put together in brackets the Korean characters, yet still, sorry for the limitations.

I will write this in two parts.

To begin with, I would like to start with a brief account on Korean history. This will help understand some common sense of history for Korean people, South or North alike. In 1910, August 22th, Imperial Japan forcefully colonized Daehan empire(대한제국, elongation of Chosun dynasty). I would not cite the long history of cruel Japanese oppression, and the fight for independence; it would require a whole book just even to touch a single side of it.

Whilst these terrible times, Socialism(that is how history books and research in Korea puts it) began to spread even under Japanese oppression. After the biggest independence movement-the peaceful demonstration which happened nationalwide: March First independence movement of 1919, the fight for independency had begun to ignite much brighter than before; many activists sacrificed their home, family, and even own lives for their cause. And some very notable independence activists were socialists; some even led guerilla warfare in Manchuria against the Japanese.

One of these were Kim Il Sung, grandfather of Kim Jung Eun, current leader of North Korea(DPRK from now on): he had a deep relationship with Chinese communist party, was not a part of internal conflict which had severe results in Korean communist parties in colonized era, and had 4 years of education in USSR; these factors would have effected him to be nominated as a leader of new communist government in Korea, after the surrender of Japan. Though it is disputed how much credit should go to his activities against Japan in the history of struggle for independence, it still is true that he was one of notable figures in independence activity.

In 1945, Japan surrendered just after Hiroshima and Nagasaki bombing. The provincal Korean government, center of independence activity in especially in 40s, were preparing for military operation in accordance with US Office of Strategic Service to reclaim Korean peninsula, lost its goal for gaining independence with its own hand. USSR army claimed northern half of peninsula; US did the other half. After another series of dispute and chaotic struggle, shameful fight between ideology(which were happening even in the era of Japanese colonization between independence activists), South Korea; Republic of Korea(in ROK afterwards) erected its own governement with aid of US and UN, in 1948, August 15. DPRK was erected in same year, September 9; though it is almost certain that USSR was already planning to erect its own government with Kim Il Sung on top, as noted above. Then came the Korean war in 1950, June 25, by an unnoticed invasion of DPRK; after the end of war in 1953, ROK and DPRK completely turned apart.

From here, there rises a key point in defining Koreans, for either South or North. This is a portion of ROK constitution, Directly retrieved from an official government translation:

PREAMBLE

We, the people of Korea, proud of a resplendent history and traditions dating from time immemorial, upholding the cause of the Provisional Republic of Korea Government born of the March First Independence Movement of 1919 ... having assumed the mission of democratic reform and peaceful unification of our homeland and having determined to consolidate national unity with justice, humanitarianism and brotherly love, ...

Article 4 The Republic of Korea shall seek unification and shall formulate and carry out a policy of peaceful unification based on the basic free and democratic order.

This is a portion of DPRK constitution, also retrieved from ROK government but it has a file format which only Korea uses in the world:

Preamble

... The great chief(수령) Kim Il Sung, and the great leader(령도자) Kim Jung Il are the ones whose grace cherished the Korean people forever(민족만대의 은인) for founding the immortal deeds done for acheiving the grand work of Motherland's unification(조국통일위업실현). ...

Article 9 The DMRK fights in order to strengthen the people's government in the northern peninsula and ... Under the codes of independence, peaceful unification, and Korean peoples total harmonization(민족대단결) to achieve the Motherland's unification.

This became too long for an introduction, but I think it would help shape some of our identity: We think that we were not seperated with our will. It was an unfortunate intervention of foreign power that segregated and created deep gaps between us. And thus, our goal is a peaceful unification and harmonization of both of peoples in our lands; of course, ROK and DPRK has different viewpoint on what power is responsible for this tragedy, and what political basis a unified Korea should have, but still.

We think us as the same people, sharing the same blood-and I beleive you can surely refer these from even the emotionless constitutions. Then what basis do we share, though we have different ideologies and had 70-year old bloodshed? From what base must we build our unification? Our history and our culture, namely the culture of 한민족.

This would be useful for you to understand the following informations about DPRK's viewpoint toward classical literature.

Reference: 김일성 항일무장투쟁 신화화에 대한 연구 (Research on Idolization of Kim Il Sung's Anti-Japan millitary actions. Research funded by Korean government and distributed by government)

I'm not qualified to answer the main body of your question but I think I'm qualified enough to answer the first, suggestive part of your question about the supposed lack of Soviet censorship of Russian classic literature. In short, you're wrong.

For example, in the late 1920s the Soviet authorities ordered to take away Volume 7 of The Complete Works of F.M.Dostoyevsky from public libraries, because Vol 7 contained his novel Demons which the Soviets declared to be "decadent" and "full of nonsensical mysticism". In fact, until the 1980s Perestroika Demons were only published as part of Dostoevsky's texts compilations, never as a standalone book. In 1935 there was supposed to be published two-volume edition of Demons but only the first volume was published (and later banned from distribution).

Fyodor Tyutchev, one of the Russian poets who is considered classics in Russia (but probably not in the West), was heavily censored in Stalin's time. Some of his political poetry wasn't published at all, only his poetry about nature was welcome. For example, his December 14, 1825 verse is mostly unknown even to Russian public to this day because of publishing difficulties in Soviet Russia. You see, Tyutchev heavily criticizes the Decembrist Revolt of 1825 that was looked upon mostly favorably in Soviet history books.

Nikolai Gogol is another name less known in the West than in Russia; in Russia he is considered one of the big names of the Golden Age of Russian literature. One of his less known (but incredibly important for understanding Gogol) works is Mediations on the Divine Liturgy. One of the reasons why it's less known is that it was never published in USSR until 1990.

Pushkin's Eugene Onegin was heavily censored in Soviet Russia, with many cuts done from ideologic perspective by soviet editors.

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In conclusion, I have to ask, where does this Western idea that Russian classics wasn't censored or suppressed in USSR come from. I've seen it before, there has to be some source for this fallacy.

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sources:

Блюм А.В. - Русская классика XIX века под советской цензурой (по материалам секретных архивов Главлита 30-х годов) / Russian classics of the XIX century under Soviet censorship (based on the 1930s Glavlit's secret archives) by A.V. Blum, 1998.

Емельянов Б.В. - Цензура философской литературы в России: от века серебряного к веку железному / Censorship of philosophic literature in Russia: from the Silver Age to the Iron Age by B.V. Yemelyanov, 2010

Шапир М.И. "Евгений Онегин": проблема аутентичного текста / Eugene Onegin: the problem of authentic text by M.I. Shapir, 2009