2002 lincoln navigator alternator

Last week, by all appearances my alternator seemed bad, i.e., would not charge battery, and the vehicle would eventually lose all power. I replaced the alternator with a remanufactured from a discount auto store, and the vehicle ran for two days, and then the same thing happened. I took the alternator back had it tested, and it tested good. However, I am told that in some Lincoln's if you do not replace the alternator with the OEM's alternator, that it may not work. I need to know how true this is as I have replaced the battery, checked all grounds, and even did the dealer trick with the light bulb looking for excessive draw on the battery by pulling fuses. HELP!!!