Imo, as it's written, it is false. Sutton did not respond to Duke ER at 1:22 in reference to a rape. I se no other way to read it, and I've read it all I want to. It's false, imo.
"On March 14, 2006 at approximately 01:22 hours I responded to Duke Emergency Room in reference to a rape."
I agree with your interpretation 1:22 is the time SHE responded.
But she probably wrote it wrong, she has no reason to lie.
(I have been guilty of that, also)