Regardless of what she tells you, you want to assume that there are other people in the equation and proceed as such. A verbal commitment or even marriage is no way to guarantee that she will not hook up with other guys or—more importantly—that she will not lose attraction for you. You must continue to keep her interested at all times. One of my basic tactics for relationship management is that I assume there are two other dating prospects for her in the picture.
I talk about it here: My basic assumption is that she is seeing two other guys who do not have any game. This basic assumption keeps me on my toes without making me jealous.
At the same time, I assume those other guys have zero game. When you assume this from the start, it makes it a lot less likely that if you hear about another guy, you will all of a sudden start to get jealous and insecure. What could do to cut off that behavior from the start, without getting upset? Maybe you got needy or showed too much concern about other guys in the picture. Maybe you pushed the relationship forward too fast and made her feel crowded instead of letting her come to you.
Maybe you let her take the lead once too often. These are the root causes for women cheating. It can come from insecurity. Or sometimes it can come from simple curiosity. You see her texting on the phone and you wonder, is she texting a guy? A while ago I was dating a girl and stumbled onto her online dating profile. I was very tempted to check how often she logged on and other things. Even taking one step in that direction is suicide. It leads to more checking. You become needy and try to account for her time.
Who was she with? She mentions a guy at work and so you interrogate her about it. Even if you could, she could still find some way to meet with a lover without you knowing if she wanted.
Your mind creates imaginary possibilities. The worst part is that it can be a self-fulfilling prophecy. She sees your insecurity and starts to lose attraction for you. Or she feels crowded by your jealousy, and so she does cheat on you. Or she uses your expressions of weakness and jealousy as a wedge to get what she wants from you before leaving you.
What she says with her words do not in any way necessarily correspond to her actions. Often times they are a smoke screen. Her words can almost always be safely ignored in lieu of her actions. You can start with some of these articles.