@HDT
I think it's wrong to say that going to film school = not making films because in any of the major film schools in the US, we make films quite often. I got to Chapman as an editor and in the 1.5 years I'm there, I've made 7 small films, 1 short film (another in pre production, going into production next week), 1 longer film and this is all working off the same professional workflow.
In fact I was in charge of everything from capturing down to dvd authoring and design. with the exception of color correction and sound design (cine and sound designer's job respectively).
Yes you can go out and make movies straight off the bat with the money you spend to go to school, but what you don't get is the chance to network with people "in your generation" which will build a stronger network that meeting random people and getting odd jobs off craigslist. There is also the point of the professors who are available to help you at school. The majority of these professors have experienced and/or still experiencing the industry.
For example, my editing professor is Paul Seydor and he's still actively editing films in the industry.
Also, when you're at school, especially ones that are known for film, the career center usually have a specialist in the film industry who can help you get connections through the school's internship/job finding network. It helps when you have on your resume that you come from a good school and get help building your reel in the process
EDIT: When you talk about Jim Jarmusch and NYU, You also have to realize the difference between east coast film school and west coast. NYU is known for the avant garde style of film making while West coast schools are usually pushed towards the entertainment and story concept. Don't make the assumption that all film schools have the same exact mode of thought. That's like saying Business school in NY is the exact same as ones in Cali because in truth, they have very different specializations that are unique to their region.