Just how great is Sweet Brair College in Virginia?

I have an acquaintance who says that this college is, quote, "almost Ivy League" and that it has an "Internationally respected equestrian team," but I'm curious if she's twisting the truth... or even flat out lying. Now, I'm not an expert on schools or anything, but it seems like any school who calls themselves a college instead of a university has lower rankings... I've heard that the four basic levels of post-high school academics are (1) community colleges (2) universities (3) "Big Ten" schools (4) Ivy League schools. If this is true, how is SBC even close to Ivy League? Could you please help me out by giving me the details on the academics and athletic programs (specifically the equestrian team) of this place? Thank you so much!