Even with a sponsoring institution, a student visa is a non-immigrant visa. Therefore, she would have to show ties to the foreign country, having a parent who is an LPR does not do much to help that case. USICS does not issue visas, the State Department does. Pleading ignorance to USCIS will go nowhere, as for pleading ignorance to State, they have probably heard every excuse imaginable; so pleading ignorance to them will probably go nowhere also.