MANY students are still accepted with later interviews -- and I think you will find that is the case *especially* at high-tuition schools, such as NYU and BU. The bottom line is that students will typically go elsewhere if they are given an opportunity for lower tuition. Many students have NYU and BU as their top choices, and those students will snatch up their seats early -- but many seats at these schools and others are still up for grabs in early spring.
It is sort of cool having an interview late, because I'm sure you'll hear from the schools soon after that. Some of my interviews made me antsy because I had to wait 4+ months to hear from the schools because I interviewed so early!
Congrats on your interviews. NYU and BU are find schools!