The agreement to pay the hospital bill could very likely be seen as an admission of liability. The neighbor could later sue for pain and suffering and emotional distress, as well as any other specific damages, such as lost wages or other expenses. If you do go through with paying the bill, I would have the neighbor obtain the bill, give you a copy, and then pay the neighbor the amount of the bill. The hospital should not give you the bill without a release, and may or may not accept direct payment from you on an account that is not yours.
The foregoing is intended as legal information concerning the question asked, but is not intended as legal advice upon which the requesting party may rely in guiding their actions. Rather, the requesting party should consult an attorney for a personal consultation and advice for a full consideration of their situation and rendition of legal advice.
Areas of practice listed are are areas of concentration in my practice. I am not board certified in any of the listed areas, and by listing them and describing my practice I am merely describing my experience and the nature of my practice.