The first thing we need to do is get "Soviet Union" completely out of the question: there was no Soviet Union in 1905, and the Bolsheviks wouldn't get power until 1917, which was on the other side of World War I. In 1905, we're very much talking about the Russian Empire under Nicholas II.

Second point worth noting is that the United States did have a treaty with Korea, namely the 1882 Treaty Between the United States of America and the Kingdom of Chosen. This was a very broad treaty and one of the first international treaties negotiated by the Korean Joseon Kingdom (it was actually written in English and Chinese) in the modern period. While it very specifically focuses on issues of trade and treatment of respective citizens (among other things it provided extraterritoriality for US citizens, and forbade American export of red ginseng from Korea), it does have a general clause in Article I worth quoting:

"If other powers deal unjustly or oppressively with either Government, the other will exert their good offices, on being informed of the case, to bring about an amicable arrangement, thus showing their friendly feelings."

Again, this is vague language. It indicates that the United States would assist Korea diplomatically in resisting encroachments by other powers, but falls far short of pledging to defend Korean sovereignty. This treaty did not keep up very well with events in Korea, as it was invaded in 1894 by Japanese forces in the First Sino-Japanese War, which established Japanese predominance in the country and ended its tributary links with Qing China. Korea would serve as a staging area for the Japanese military in the 1904-1905 Russo-Japanese War, but it should be pointed out that it was not formally annexed until August 1910, so this was after Russia and Japan had signed the Treaty of Portsmouth in September 1905.

Anyway, on to TR's thoughts about Russia, Japan and Korea. Roosevelt thought very poorly of growing Russian influence in East Asia, notably its expansion into Manchuria and its occupation of Port Arthur on the Yellow Sea. He cared less for Russian autocracy and for the tsar, whom he denounced as a "preposterous little creature." Initially, Roosevelt much favored the Japanese attack on Russian forces in 1904, stating that the Japanese were "playing our game" and making noises about the Japanese, with their military and economic prowess, being a desirable addition to "our civilized society". Of course, a more pragmatic benefit also was that Japanese aggression against and expansion at the expense of Russia turned their attention away from American colonies in Hawaii and the Philippines.

Roosevelt was mostly hoping for both sides to fight themselves to a draw, but when it became clear that Japan was on the verge of winning a decisive victory, he decided to push for peace before Japan got "a big head". Roosevelt began to push both sides towards the negotiating table, much to his increasing private frustration (TR on the Russians: "capable of literally fathomless mendacity"; on the Japanese: "an oriental nation, [whose] individual standard of truthfulness is low". The Russian naval defeat at Tsushima, coupled with increasing financial strains on Japan, finally led both parties to the negotiating table.

After negotiations under American auspices (Roosevelt was not personally present), an agreement was finally reached at Portsmouth, New Hampshire - Japan gave up claims to indemnities, received Port Arthur and southern Sakhalin, secured a sphere of influence in Korea, and agreed to share control of Manchuria with Russia.

The Japanese were frustrated with what was effectively a compromise after numerous smashing military victories, and national mourning was declared. There were even demonstrations against the treaty, leading to the American legation in Tokyo being surrounded by mobs.

Now here is where your colleague might be on firmer ground. In July, 1905, William Howard Taft had been dispatched to Japan to conduct secret negotiations with Japanese Prime Minister Taro Katsura. This agreement (it wasn't revealed for another two decades) essentially gave Japan free hand in Korea in exchange for it disavowing any aspirations or pretensions towards the Philippines or Hawaii, and this is where the United States was effectively ignoring its obligations under Article I of its 1882 treaty with Korea. In November of that year the Koreans even requested that the US fulfill its obligations, and Roosevelt demurred, stating that the Koreans would in any case be unable to defend themselves (although in the defense of the United States, there was a limited amount it would have been able to do - it was far from a military superpower in 1905). Further secret agreements in 1908 would confirm US recognition of Japanese spheres of influence in Northeast Asia.

So, in summary - Roosevelt did turn away from treaty obligations between the US and Korea, although these obligations were somewhat vague and the US would have had limited means to "get tough" even if it wanted to. It's also worth remembering that secret treaties between great powers delimiting spheres of influence were par for the course in the period's diplomacy. While Roosevelt opposed Russian influence in the region, he was much more concerned about diverting Japanese influences away from American colonies than Russian containment, however.

Source

George C. Herring. From Colony to Superpower: U.S. Foreign Relations since 1776