I need some advice from some of you who are more familiar with CO's policies than I am. Here's the story:

My cousin (not much flying experience) was supposed to fly tonight (Thurs. 3/10), PHL-CLE, flight 1600 (6:10 PM) for an interview tomorrow. Due to work issues and traffic, she arrived at the checkin desk at 5:43 PM. The ticket had already been purchased, and she did not have any baggage to check in for the flight. However, the customer service agent at check-in (male, but she didn't get a name) denied her the chance to board the flight, saying that she was checking in too late. As a result, she will not be able to leave PHL until tomorrow morning, and get to CLE at 8:11 AM (and her interview is at 9 AM, in Wickliffe). I took a look at CO's contract of carriage and it says that the cutoff is 15 minutes (at the gate) as long as the ticket has been purchased and no baggage has been checked in for the flight.

(Yes, I know that she could have - and should have - checked in earlier, and online, but I'm arguing a policy that they have.)

While the argument of "would she make it through security and to the gate in time" could be debated, I want to know the following:

Do you have any suggestions for a viable solution to the problem (for example, compensation for her being involuntarily denied boarding)? If so, who should I contact in order to deal with the issue?

Thanks for any advice you can give to me.
gmax58