The reason Columbia guarantee's housing is that it's cheaper to live on campus than to find an affordable NYC apartment: NYC Rental Process | CU Facilities - Housing
"New York City's rental market is different from most other cities. Most landlords require that your annual income be between 40 to 50 times the monthly rent. For example, if the monthly rent were $3000 per month, you would need to show income of at least $120,000 per year.
Landlords may accept roommates' combined incomes to determine financial qualification for an apartment. If the rent is $2500, the landlord would typically want to see a total income of $100,000. If both roommates earn at least $50,000 annually, they could "combine" their incomes in order to qualify for the apartment. If this is not permitted, you will be asked to provide a guarantor or lease co-signer, a person who accepts financial liability in the event you or your roommate fails to pay the rent.
Landlords require that guarantors earn between 75 to 100 times the monthly rent in annual income. This means that for a $3000 apartment, a guarantor must show income of at least $225,000."