In a PBS documentary, Steven Ambrose claimed that the Cubans were far from victory at the start of the war, and implied that this justified American involvement. Is there any truth to that statement?
This is a question which has also bothered me a great deal. Despite having read quite a bit I cannot give a definitive answer, but perhaps I can offer the elements which both sides traditionally use to favor their arguments.
There are essentially two main camps, which are inescapably tied to two political narratives about the island's relationship with the USA.
Let's call the narrative you came across the Gratitude narrative. In essence, the Cubans were stuck in a second independence war, without hope of victory (the first independence war, 1868-1878, had lasted a decade and obviously ended in failure). Here the US struts in and saves the day, because Cuban guerrilla fighters were unable to face the amassed might of the Spanish army on land and, since they had no navy to speak of, couldn't hope to fight the Spanish at sea. This is frequently used not just by American historians but also American politicians, with the latter using it as part of a political narrative which suggests that Cubans owe the US a debt of gratitude and that certain nationalistic actions/policies by Cuban governments were/are signs of ingratitude.
Opposed to this is what I will call the Nationalist narrative. This is particularly popular among Cuban historians of a nationalist mindset who attempt to frame the war as already won in an attempt to undermine arguments of Cuban indebtedness to the US. In pre-1959 Cuba, the historian Emilio Roig is a good example of this. More recent historians, like the now deceased Oscar Loyola Vega have made similar statements quite publicly. Cuban politicians who favor this narrative also tend to enter the realm of conspiracy theories, stating that the destruction of the USS Maine was actually a black flag operation by the US so that we could have casus belli against Spain once the Cuban independence movement had already softened them up for us.
As you can see, this is treacherous ground because you're dealing with a highly politicized issue with both sides having a vested interest in pushing their narrative, regardless of what the facts may be.
According to books I have read on the period, the situation in the war was as follows:
By 1898 the Independence movement largely controlled the countryside but was unable to take major cities, like Havana or Santiago, much less hold them. The independence movement had lost several of their best in battle, such as the intellectual architect of the second independence movement, Jose Marti, and the popular military leader, General Antonio Maceo. While Rebel forces were able to send out important expeditions into the Western half of the Island, for the most part the war was contained in the Eastern half (with a huge defensive line, trocha, right down the middle, protecting the prosperous West). Spanish popular opinion does not seem to have been swayed by the independence movement to the point of supporting independence for Cuba as a final solution to the problem, although greater colonial reforms which modernized and democratized its institutions was seen as a viable reformist option. The Spanish military, both on land and at sea, was intact. The Cuban civilian population, the main supporters of the independence movement, had also been dealt huge blows with the Reconcentracion (forced urban concentration of urban population, which killed tens to hundreds of thousands of civilians) and the policy of the tea ("torch"), by which valuable sugar cane fields were set alight so as to take away Spain's main source of income from the island.
My conclusion is that given the facts that a) Spanish opinion remained opposed to independence, b) Spain's armed forces remained intact, c) the Independence movement had lost many of its most important figures, d) Independence movement was unable to take and hold major cities, e) the war seems to have stagnated, to the benefit of the Spanish, that the war's outcome was anything but 'already won' and that it could have quite possibly ended in defeat for a second time, followed by even more Spanish colonial reforms.