You say the phone is a Note 4 for sure, but what have you done to verify that it is not a chinese fake note 4 knockoff. These "fake" note 4's look and feel so much like the real deal that until you start having noticable software and hardware issues it is difficult to tell at first look.
The best and only 100% accurate way to tell if it is a fake chinese knockoff or a genuine Samsung product is simply to put it into download mode. You do this by shutting the phone off completely, hold down the volume down, home and power buttons until the display comes on.
The fake asian knock off will just display some chinese symbols whereas EVERY authentic Samsung mobile device that can be put into download mode will display "Warning!!" at the top and will have a yellow triangle with an exclamation point on the screen somewhere as well.
I know you said it's not a fake but I looked at 4 different "Note 4s" from Craigslist and they all seemed legit even after playing with them for a few seconds but all 4 were fakes and at least 3 of the people selling them I genuinely believe did not know. Just thought I'd share that in case you hadn't dug very deeply to double check the device's authenticity.