The question of the name
Though it is not only politically incorrect but factually incorrect to refer to the conflict as the "Philippine Insurrection" (1899-1902), much can be learned from an examination of "why" it is referred to as such, even today.
At the time and for years (I note that as of this submission, www.britannica.com has the entry under " Philippine-American War," yet also refers to it as an "insurrection" in the article) it was referred to as an "insurrection." The Filipinos deny this to be reality. In order to be an "insurrection" (which their revolution against Spanish colonialism was), they would have to be rising up against a civil/political/military authority under which they lived—I am aware of Webster's distinctions, but since dictionaries reflect usage more than actively defining words, I feel on safe ground here. The United States had no such authority (except in the sense that it assumed and designated it unto itself).
When Spain surrendered at the end of the Spanish-American War (which, in the Philippines, included the native people as a major player), the US only occupied the city of Manila and as part of the peace protocol, was only given that (and the harbor and bay) as occupied territory—this, of course, was meant as only a temporary measure until the fate of the islands would be decided. Except for Moro-controlled Mindanao, the rest of the islands were under the control of the Filipinos—Filipinos who had declared independence from Spain two months prior to the signing of the peace protocol.
This was ignored or forgotten and when the Treaty of Paris was created and signed, ending the war and—among other things—ceding the Philippines to the United States (along with a $20 million "gift") the Filipinos were not allowed to be part of the negotiations. With the treaty, the Philippines became an American colony (though without the start of the war, ratification of the treaty might not have taken place and the Philippines could have gotten its independent nation status that had gone unrecognized by all the countries of the world). Further, not only did the treaty become ratified after the war began, Spain didn't ratify it until over a month later.
Other factors were involved. One is the way it had been reported to the press which was entirely in terms that read "insurrection." This was, in turn, disseminated and became the way the conflict was viewed by a public that couldn't know better regardless of how they might have felt knowing the facts of the matter (which were "fudged" as well, making it appear that the Filipinos had fired the first shots that began the war). About 12 hours after those first shots had been fired, a cable was sent stating that " insurgents have inaugurated general engagement yesterday night which is continued today" and that "insurgents have been driven back and our line advanced." The "fact" that it was an "insurrection" became accepted. And perpetuated. President Theodore Roosevelt's proclamation ending the war refers to the conflict using that term or a variation on the root eleven times; the only thing close to "war" was a reference to "acts in violation of the laws of civilized warfare."
The other factor, and arguably the least excusable, is that by calling it something other than "war," allowed the US to avoid giving combat pay to the soldiers. Regardless, it was firmly entrenched well before the end of hostilities (which lasted a few years beyond Roosevelt's 1902 proclamation) and remained the "received" title of the conflict.
(Sources: http://phil-am-war.org, www.filipino-americans.com, www.ualberta.ca/~vmitchel, www.sfgate.com/cgi-bin/article.cgi?file=/chronicle/archive/1999/01/31/SC16131.DTL, www.sfgate.com/cgi-bin/article.cgi?file=/examiner/archive/1999/02/04/EDITORIAL11417.dtl, www.philnewscentral.com/philrev.html, gopher://gopher.umsl.edu/00/library/govdocs/armyahbs/aahb4/aahb0247, gopher://gopher.umsl.edu/00/library/govdocs/armyahbs/aahb4/aahb0248)