Well in a sense China wasn't really saved by the US - the more important factor in its non-partition was the mutual suspicion of the Great Powers and ability of the Qing court to play one off against the other.
One could argue that the 'Scramble of China' was well underway by the late 1890s or even the 1880s, with the development of 'New Imperialism' and the failure/perceived failure of the Self-Strengthening Reforms. Certainly by 1885, France was obtaining railway concessions in the Chinese southwest and in 1897 Germany occupied Jiaozhou (Qingdao). 1898 saw more concessions with Kwang-Chow-Wan (Zhanjiang) to France, the Hong Kong New Territories and Weihai to Britain, and Lushunkou (Dalian) to Russia. Britain and Russia were already exchanging sphere-of-influence guarantees in 1899, the same year that the Open Door policy was issued.
And in any case, it's not exactly right to read the Open Door policy as a 100% 'anti-colonial' measure. America demanded equal opportunity for ordinary trade, not for investment. Shandong still had to rely on German capital, Yunnan on French capital, the Yangtze on British capital. And when the Russo-Japanese war ended in 1905 Roosevelt was more than happy to transfer Russia's rights in Manchuria to the Japanese - hardly anti-colonial behaviour.
So basically what I'm trying to say is that if the Europeans really made an effort for colonies in China, they could have gotten them before 1899; and in any case, this wasn't something that really concerned America as long as the Europeans colonized China with some regard for US interests.
The more likely reason for why Europeans didn't colonize China is because they were mutually suspicious of each other's intentions, and the Qing court used this to its advantage as best as it can. Yes, Germany obtained extensive rights in Shandong in 1898 - but this was counterbalanced by the Chinese 'lease' of Weihai to Britain, which threatened both Russian and German spheres of influence. Similarly, British influence in Guangdong was counterbalanced by French concessions which specifically forbade Qing China from making any non-French concessions in lands bordering Indochina. The most aggressive movements by Japan and Russia were moderated through mutual suspicion and, in the case of Russia's attempted annexation of Harbin in 1908, the US' suspicion of both powers.
So in a sense, Western powers restrained each other in China out of a desire to not be the 'first-mover' that could end up with one power dominating all of China, which would be tremendously detrimental to everybody's interests. Of course, this situation couldn't last forever, and certainly by the late 1900s we see concerted movements by European powers (the Four-Power Hankou Railway Concessions) that could have eventually led to a partition of China; but WWI intervened to put an end to that.