Yes, you are correct in that this girlfriend was too quick to give you a key to her place. From the little you have shared it sounds like this girl is still VERY naive and doesn't understand boundaries very well either. If she cheated on you it's important that you understand how that is really saying more about her than how deserving you are of having someone care about you and your feelings. Often a person who is naive like this tends to just love being loved and admired but still doesn't understand what it means to actually slowly develop a relationship that involves being able to actually understand the other person better.