Are doctoral programs in the USA like a Masters leading into a PhD? Before I begin, feel I should make it clear that I have no doubt that undertaking a PhD. anywhere, let alone at Harvard, will be a difficult and strenuous task!

To briefly explain, I have graduated with a good Bachelors of Arts from the UK, and am set to do my Research Masters in Holland. However, I have been in contact and have contacted the literature faculties in Harvard, who have been very encouraging but, to be honest, the system itself seems very different.

To clarify, I'll copy in some of what my (possible) supervisor has emailed me:

Our students enter the program, take two or three years of courses, and only then settle on a dissertation topic and choose a committee of three faculty -- one primary advisor and two other readers.

This sounds at once much more fluid and liberal a way of doing things, but, considering the ridiculous costs of studying in the USA, I'm not sure how leisurely that would be in reality! Should I assume that Doctoral programs in the USA are like a Masters leading into a PhD? Is there a scholarship available for both of these? 
Has anyone reading this had any experience on the matter, and can relate more clearly how this process works, and whether exceptions are every possible?
The quoted description is pretty standard for how Humanities departments in the US work. Most students entering Humanities PhD programs in the States do not have MA degrees, although a significant proportion of those from the UK do. It would be unlikely that you could skip those first 2-3 years of coursework. Even if you could, it would put you at a serious disadvantage even if you knew in advance what topic you wanted to research. A 1-year UK MA degree, just does not prepare you to the same extent as 2-3 years of coursework.

As for funding, the top students are likely guaranteed funding for some number of years. The funding will likely require some teaching. The teaching maybe in the form as a TA, but is likely to be much more extensive and require you to design and run a large undergraduate lecture class. For those students, the funding will cover tuition and a stipend. Those without guaranteed funding can still get funding for teaching, but you cannot count on it. How tuition is handled depends on the university/department and where you are in the program.

In the Humanities, it is unlikely that any supervisors will have grants that pay for PhD students, but there are grants that you can apply directly for. Some of these cover students in the first few years, but most are for more senior students.

For US PhD programs in the Humanities, unlike in the Sciences, funding should play a huge role in your decision of where to go. In the Sciences, everyone essentially has funding that covers tuition and living expenses and very little teaching. In the Humanities, self funded students and students with with huge teaching requirements are common. There is a huge difference in productivity and happiness between those who have to take out loans, that they will likely never be able to pay back, or teach and those who do not.