The UN-backed election that you're mentioning is known as the '1948 South Korean Constitutional Assembly election' or more commonly as the '5.10 Election'. The reason why this election was so important was that it was the election that literally decided who controls the national assembly(the congress/parliament) of Korea and later on, deciding the first head of state of Korea. In this case, deciding the president.

"Larger popular outvoting the communists?" - Yes. This part is indeed true. United Nations General Assembly Resolution 112 was the UN resolution that decided the elections to happen in Korea. A part of the resolution states:

"2. Recommends that the elections be held not later than 31 March 1948 on the basis of adult suffrage and by secret ballot to choose representatives with whom the Commission may consult regarding the prompt attainment of the freedom and independence of the Korean people and which representatives, constituting a National Assembly, may establish a National Government of Korea. The number of representatives from each voting area or zone should be proportionate to the population, and the elections should be under the observation of the Commission;"

As we can see, the United Nations "made" the elections to be a first-past-the-post system by dividing the country into a bunch of electoral districts. Since that says the districts should be proportionate to the population, the more an area has people, the more districts they get. Thus, more seats in the national assembly.

South Korea is commonly known to have hit 20 million in population in 1949. North Korea's exact population is unknown (even today's population numbers are just estimates by the UN and the Ministry of Unification in South Korea), but a 2010 paper by the Korean Academy of Social Sciences states that the population of North Korea in 1948 was about 9.5 million. In theory, if all of North Korea voted for the communists, they'd only take over about 1/3 of the seats. This national assembly later on votes for the first president of Korea, and they would definitely be unable to elect a communist leader like Kim Il-sung if they had only a third of the whole assembly.

So yes, North Korea would obviously be unable to have a grip over the national assembly. But that's not the whole story.

Both the United States and the Soviet did actually agree upon a 'democratic process' for an independent Korea. During the Moscow Conference in 1945, the US, UK, and USSR agreed upon this resolution (known as the Report of the Meeting of The Ministers of Foreign Affairs of The Union of Soviet Socialist Republics, The United States of America, The United Kingdom) and they wrote it down on the "III. Korea" section of it:

"It shall be the task of the Joint Commission, with the participation of the provisional Korean democratic government and of the Korean democratic organizations to work out measures also for helping and assisting (trusteeship) the political, economic and social progress of the Korean people, the development of democratic self-government and the establishment- of the national independence of Korea. "

However, the Soviet Union wanted a Soviet-influenced Korea and the United States wanted an American-influenced Korea. The Cold War was on its first steps on becoming a thing between the two superpowers. Continuous disagreements between the two states and the different ideological backgrounds were big factors.

One of the largest disagreement happened during the US-Soviet Joint Commission in 1946. The Soviets claimed that only the Korean groups who supported the resolution of the Moscow Conference should be consulted for the discussion of creating the independent Korean government, while the Americans claimed that certain groups shouldn' be excluded because they disagreed with the Moscow Conference.

Not only that, but the division between Left-wing Koreans and Right-wing Koreans were also really getting extreme. One of the most notable events that occurred at this time was the "Jeongeup Remark(정읍발언)", which was an incident where Korean right-wing leader (and later on becomes president) Rhee Syung-mahn(리승만), who has become mad after seeing the US-Soviet Joint Commission fall apart due to the two sides failing to agree with each other, claimed that at this situation, the southern half should form its own committee and remove the reds in the north. This event is well-known because it's the first moment when a "one side only government" was mentioned. Generally, the left agreed on an International Trusteeship system and pushed Korea to become a trust territory controlled by the two foreign powers, but the right disagreed want wanted immediate independence.

The thing is that the left-wing/Soviets and right-wing/Americans failed to agree on anything by this point. (and later on, war) And since the Cold War really began at this point, the two sides weren't able to trust each other. This is why when the United Nations Temporary Commission on Korea tried to enter North Korea, the Soviets blocked them. The Soviet's pretty much disagreed with the UN/USA's direction on this election.

*sidenote/fun fact*: The South Korean National Assembly, despite being a unicameral one, actually has a second chamber. The first chamber (the one actually being used) has about 300 seats and the second one has 200. The 300 represents the people of South Korea and 200 for North Korea. The National Assembly building, during its construction, actually made this chamber to prepare for unification. If the Soviets had just let the UN in, maybe these seats could be all filled up. (the second chamber is now just used for the budget committee and other minor events)