@FutureWordsmith I’ve never understood that “backdoor” comment. This would imply that some secret is involved. Admission requirements etc., are all out there in the public domain. And there is a joint faculty committee that periodically discusses admissions policies etc (not to mention that Barnard and Columbia share the same university President).
As for why Barnard is viewed as part of Columbia, the reason is simple: because it is. People go to Barnard largely because it is a women’s college that is part of a major university. Barnard is proud of being a distinctive member of the Columbia community but even its main gate says, “Barnard College of Columbia University”. That IS its identify. That is what has always made it different from the other women’s only" colleges. I don’t see how being part of a incredible research university in any way detracts from Barnard’s standing.
The rankings are a bit of a nonsense. As many people have pointed out, Barnard does not confer degrees. The degrees are conferred by Columbia University. Barnard College and Columbia College students get the same degree and the same diplomas. And the vast majority of courses taken by Barnard College are offered over by Columbia.