An offer of judgment is not an admission of guilt, although, there is no reason why a party can't admit liability at the same time they are making an offer of judgment. Typically, an offer of judgment is a tacit concession by the defendant, that a) he can't win the case or b) he can only win by expending a huge amount of money, which makes settlement appropriate. If your wife insists on the other side admitting liability, and they won't do so, she can reject the offer and proceed to trial. Depending on the circumstances under which she rejects the offer of judgment, she could become liable for the other parties costs as well. Listen to your attorney. There are never any guarantees in litigation, and receiving money is a whole lot better than not receiving money.
If you'd like to discuss, please feel free to call.
Gold, Benes, LLP
1854 Bellmore Ave
Bellmore, NY 11710
Email - Jgold@goldbenes.com