In short because it was internationally recognized and privately owned by Leopold II via the International Association of the Congo and it was not colonized nor subject to the nation of Belgium. In fact it wasn't called the Belgian Congo until after 1908 when Leopold was forced to give it up and Belgium annexed it. Under Leopold it functioned as an independent corporate state initially through the non-governmental International Association of the Congo which he owned the majority of stock in and eventually formed the Congo Free State in 1885 which he became sovereign of, after international recognition.

The horrific atrocities that were committed in the Congo Free State were done during Leopold's ownership (1885-1908).

King Leopold II was a constitutional monarch (whose father's first wife, if she had lived, Princess Charlotte of Wales would've become Queen of the United Kingdom after George IV), and had a minor role in the day-to-day governance of Belgium, but was obsessed with Belgium becoming an economic force and taking its place among Europe's colonial powers. He believed that only in an overseas empire could a small nation like Belgium could become great. Nations like Portugal and the Netherlands were examples of this. Both of these nations held colonies and trading posts from the Caribbean to East Indies and Africa. They created great trading empires and controlled vast tracks on territory that were larger than their own nations. Leopold sought the same for Belgium.

From the start of his reign in 1865 Leopold sought to acquire the territories of waning colonial empires. He sought to purchase the Philippines from Spain but he did not have the funds. He then tried unsuccessfully to establish the Philippines as an independent state which would be ruled by Belgium. He also attempted to acquire Borneo from the Netherlands and buy territories from Argentina. Through all of this the Belgian parliament gave Leopold no support. Leopold then decided that he didn't need Belgian support and took on the effort to establish colonies himself as a private citizen.

After this is when Leopold shifted his focus to Central Africa. I think we forget in this day and age about how little geographically was known about the world in the 19th Century. Large parts of Central Asia and Africa were unknown to the Western World. (If you are interested read The Great Game: The Struggle for Empire in Central Asia it is an older book but a great read that illustrates this concept I am talking about). In the 19th Century much of the African coast was known but the interior was still unexplored. Explorers over decades began to discover the interior by navigating Africa's rivers. The Niger River, the Zambezi, and parts of the Nile had been navigated (up to a certain point) but the Congo remained a mystery. A large reason for this is because you cannot sail inland on the river from the ocean, the Congo flows to the Atlantic and the lower river is unnavigable, and travelling overland was then near impossible. That was until Henry Morgan Stanley went to search for Dr. Livingstone. After this famous expedition the NY Herald and Daily Telegraphed financed an expedition lead by Stanley to complete Livingstone's mapping of the African Great Lakes and Central African Rivers. Stanley after much hardship was ultimately successful in 1877.

In 1876 Leopold hosted a conference to stir up interest in humanitarian endeavors for Europeans to take Central Africa to improve the lives of the people there. It was at this conference that Leopold organized the International Africa Association as a means to promote humanitarian efforts in the Congo and was himself elected chairman (how lucky!). This was really just a front for Leopold and he used the association to promote plans to seize Central Africa under this humanitarian guise. Meanwhile after Stanley's return from his Central African Expedition he had been trying to stir up interest of colonizing the Congo in Britain but was unsuccessful. Leopold tried to recruit him through intermediaries several times and eventually Stanley gave in most likely because Leopold seemed to be the only one willing to finance Stanley's Congo dreams.

From 1879 to June 1884 Stanley was in the Congo paving the way for Leopold's dreams. (he was unsure who he was working for, Leopold the International Africa Association or the International Association of the Congo-- a branch off of the IAA). He built roads from the lower river to the Stanley Pool (modern day Brazzaville and Kinshasa stand at opposite sides of it), launched steamers on the upper river, established trading posts and highly dubious treaties with local leaders. With Stanley's help, Leopold was able to claim a great area along the Congo River. In November of 1879 the International Association of the Congo was established by Leopold out of the International Africa Association to further Leopold's goals and interests in the Congo and as a means to be legally and internationally recognized. This time period is most important. No one had really claimed this area, even the Portuguese had a trading post at Bomo there hadn't been any real claims or further settlement in the Congo. With Stanley building and infrastructure and establishing treaties and trade Leopold could make a strong claim to the Congo.

While Stanley was building an infrastructure in the Congo Leopold was building international support for his claim. He offered to support France's claim to the northern bank of the Congo who in turned recognized his claim to the southern bank. Leopold also enlisted Henry Shelton Sanford who was America's Ambassador to Belgium from 1861-1869. Sanford on behalf of Leopold helped convince President Chester A Arthur that Leopold's venture in the Congo was benevolent and akin to America's involvement in Liberia. He attempted to distract British detractors by promising to end slavery in the Congo. He also privately promised British merchants that they would be granted MFN (most favored nation) status while at the same time promised Bismark and Germany that all nations would be able to trade freely and no one would be granted favored status.

However, by the early 1880s greater European knowledge of Africa and the demand for resources dramatically increased European involvement in Africa. France had expanded in Northern Africa, Britain saw its vital link to India via the Suez Canal threated by France's eastward march through the Sahara, Portugal had nominal control on the coasts (Angola and Mozambique), Germany feeling vulnerable and late to the game began it own expeditions and Belgium, France and Portugal all claimed the Congo basin. This lead to Bismark calling for the Berlin Conference so that the European nations could work out a joint policy on Africa.

One of the results of the Conference was that they formally recognized the International Association of the Congo's claims in the Congo and since Leopold owned most of the stock in this company, it hence was his claims. A few months after the Berlin Conference the territories controlled by Leopold were proclaimed as the Congo Free State and Leopold as its sovereign. The US, as a result of Shelton's work, was one of the first nations to recognize it. Other European nations were reluctant to but were either not willing to take the burden of running the Congo as a colony or were happy to see their rivals denied access to the area.

However, here is the catch according to the Belgian constitution Leopold could not act as head of state of another nation without parliament's consent. He ultimately received this consent from the Belgian parliament to be the head of state of the Congo Free State.

So internationally the Congo Free State was recognized as an independent state apart from Belgium. The Belgian Parliament did not finance it nor did they administer it nor did the Belgian army police it. Of course this isn't to say that there weren't numerous Belgians who weren't involved. Belgians served in the Congo Free State's army the Force Publique, many Belgians served as the Vice Governor Generals and others within the administration, in addition to the many Belgians and other nationalities who committed these atrocities. While one can claim that the Belgians in a way are at fault King Leopold, in his capacity as the sovereign ruler of the Congo Free State, is ultimately held responsible.