When “Broken” first aired, I assumed (as I believe the audience was supposed to) that Emma was able to jumpstart Regina’s magic because she was the Savior/child of True Love/etc. And, as such, I assumed that Regina thought the same.
Except, she’s surprised that Emma has magic in “The Cricket Game”. She had no idea that Emma could use magic, and between the episodes there is no indication to Regina that Emma was able to do anything magical (e.g., she doesn’t know about Cora trying for her heart).
So when Emma says she can use magic, she’s shocked. And you can see when it clicks that it’s because she’s the Savior. Only, this implies that she’d come to another conclusion about how she was able to get the hat to work in “Broken”. A conclusion that has nothing to do with Emma being the Savior, but rather Emma being Emma.
This means that Regina had assumed that her magic was kickstarted solely by Emma touching her.
And, as we all know by now (as does Regina), magic is emotion. So Regina had not only assumed that Emma’s touch had brought about her own magic, but she had accepted that Emma’s touch brought forth emotion strong enough to power a damn portal.
Once upon a time, long ago, there was a little girl. A - a little girl who was different… Who was different from the other people in her village. She could see and - and do things that no one could understand, and that made them scared of her! She turned away from everyone and became sad and lonely, and had no one to turn to. The more she turned away from people, the more scared they were of her. And they did something terrible! They became so scared that they took her away and tried to kill her! [x]
A good friend told me retirement doesn’t suit me. And my superior told me to hurry up and catch up to him. What a bunch of jerks, eh? Even when I’m down they don’t let me off the hook. I can catch up to them even if I’m not in the military. Everyone’s waiting for me. So I’ll pull through.