I’m not sure that “both schools know that students try to use Barnard as a back door in to Columbia”. Though I have heard this mentioned in CC threads, I have been unable to confirm this elsewhere.
That said, do tell that is available at Columbia that isn’t at Barnard.
Lastly, are you aware that “Barnard students get a Columbia University diploma”
http://barnard.edu/frequently-asked-questions-8
“The only difference between Barnard and Columbia College diplomas is that the Barnard diplomas include the Barnard College seal.”
http://www.columbia.edu/cu/diploma/history.html