@George698 While I also can't speak for another host as to their charges and motivations, the host has a maximum limit of 13 people. You are asking for special treatment that goes against her house rules and parameters, and while you are confident that you and your friends will be respectful and not cause damage or disruption, the host doesn't know any of you. So it's not outrageous for her to be covering herself for such a large group that is asking for a booking outside her stated maximum guest count.
It's good that you've been upfront about the number of guests, but lying about the numbers won't bypass the problem. If more people attend than the number you have stated, the extra people could all be turfed out, as they would be trespassing. I'm sure the party you have planned would not be enhanced by having the police called, partygoers escorted off the property, or the party shut down.
And the financial situation of you and your friends is not the host's concern. She isn't your mother or a bank loans officer, she is running a business. I doubt that any of you go to Starbucks and try to haggle over the price of a coffee on the basis that you are struggling college students. If the price is too rich for your blood, look for another place that you can all afford, or maybe some community hall that is set up for large gatherings.