You have the option of going as a normal student. If you do, top-tier colleges usually look at college and AP courses taken at other institutions as a bonus towards admission.
I went to Amherst College (#1 liberal arts college in the U.S. when I matriculated), having taken courses at Harvard Extension School, UMass Lowell, and Boston University as a high-schooler. They didn't give me credit for any of them, nor for the 8 AP tests I passed. However, I was told that they were a big plus on my otherwise-lackluster application. The fact that I could take and ace college courses at other institutions was a great way to nullify the fact that I was failing my high-school courses.
My sister did courses at Middlesex Community College (again, through the same MA dual-enrollment program that I used) and went to Rice University and my wife did courses at Foothill Community College (through CA's dual-enrollment program) and went to UC Berkeley, so not an isolated experience.
It depends on the school. Dual-enrollment often does not count as entering college to the eyes of admissions committees. However, if you enter in a full-time degree program, you may be required to apply as a transfer student.
> You're a transfer student if you enrolled in a regular session (fall, winter or spring) at a college or university after high school. (Taking a class or two during the summer term immediately following high school graduation doesn’t make you a transfer student.)
> Students who have enrolled either full-time or as a degree-seeking student after leaving high school or through an early college entrance program must apply for transfer admission.
I'm not saying it's impossible. I'm saying it's just less likely. The admissions statistics for these universities show that. After all, they really only admit transfer students to fill in for students who dropped out of their school. They base class size solely on the freshmen class.
In your case, I don't think you were applying as a transfer student. You were also not going to your local CC. Those universities are a higher tier than your local CC.
In the case of "running start" the whole premise is that you have 2 years of college completed when you graduate. Not that you spent 2 years doing college courses to just restart from level 1. You can do that but I think it's a waste of resources and will unnecessarily crowd local community colleges. And it did where I went to community college. I had to deal with a bunch of 14-17 year old high school age kids. >=25% of the student body was high schoolers with some of my classes at 50%+. Gets kind of annoying when you have to constantly deal with those kids still being kids.
I wasn't applying as a transfer student, and I'm saying that it absolutely does make sense to restart from level 1 if you get into a high-tier university, and that doing so can help you get into such a high-tier university.
Yes, it does unnecessarily crowd local community college. Such is the arms race that is today's college admission's scene.
You're not considered a transfer student when you do Running Start. As long as you haven't actually graduated high school when taking the community college classes, you're considered a freshman applicant when applying to colleges. It's offered as a better alternative to just taking more AP or IB classes, which are also 'college level'.
I went to Amherst College (#1 liberal arts college in the U.S. when I matriculated), having taken courses at Harvard Extension School, UMass Lowell, and Boston University as a high-schooler. They didn't give me credit for any of them, nor for the 8 AP tests I passed. However, I was told that they were a big plus on my otherwise-lackluster application. The fact that I could take and ace college courses at other institutions was a great way to nullify the fact that I was failing my high-school courses.
My sister did courses at Middlesex Community College (again, through the same MA dual-enrollment program that I used) and went to Rice University and my wife did courses at Foothill Community College (through CA's dual-enrollment program) and went to UC Berkeley, so not an isolated experience.