Points 0 and 1 are (mostly) correct, though I don't think point 2 really has any appreciable impact on the costs.
To clarify one thing: Columbia doesn't exactly "subsidize" Barnard - in fact, Barnard maintains its own independent endowment and board of trustees. Columbia and Barnard "partner" together to provide a number of joint services (for example, Columbia students majoring in theater take their classes at Barnard, and vice versa for some other departments, but many departments exist independently at each school). Barnard retains its own independent administration for most positions; there is very little sharing of administrative roles.
Student organizations are joint-funded through student fees, and almost all are open to both Columbia and Barnard students. In fact, there was some debate a few years back about the Barnard group overseeing student organizations not contributing its fair share towards Greek life[0], which was soon rectified. It is important that fund transfers between (e.g) Columbia College and Barnard are generally not considered internal transfers the way (e.g.) Columbia College and SEAS (the engineering school) would be.
This is not unlike the situation at certain other schools like Harvard and MIT, which sometimes allow cross-enrollment, or other schools which pool resources for student activities. The main difference is that Barnard professors are awarded tenure from Columbia University, not from Barnard (which cannot grant tenure independently).
That said, I agree that Barnard's expenses are not indicative, but that's more because they share many resources with another school (Columbia) and reap efficiencies that way, not because Columbia "subsidizes" their costs. Columbia saves a lot of money from these partnerships as well, and I doubt that they would keep the current setup if they didn't feel that they benefited from it financially as well.
[0] http://columbiaspectator.com/2011/04/26/inter-greek-council-...