I really don't get the 'slippery slope' aspect of the argument.
Sure, at some point accommodating this girl may become unreasonable, but at this point no accommodations have been made.
You stop granting requests when they become unreasonable, or if you have reasonable expectation that granting that request will trigger further unreasonable requests.
e.g. You ask me to drive you to a job interview. That request does not seem unreasonable (I have time, I want to do you a favour, it's not far away), so I do it.
On the way back, you ask me to drive you to the shops. That is an unreasonable request in this case (I'm hungry, I want to go home, I have jobs to do around the house), so I say no.
It's not that driving you to a job interview was the first step on a 'slippery slope', it's just that you made one request I was prepared to grant and one that I wasn't.
Not granting a request purely based on the fear of future requests (if this hasn't been a pattern of behaviour in the past) is silly, IMO.