Peeta is definitely a character who remains true to his own principals and beliefs, even in the dangerous and life-threatening environment of the arena and the Hunger Games, where children are forced into life-and-death situations. One way that we can see this is the way that Peeta accidentally killed the girl known as "fox-face" by leaving berries out that were actually poisonous. Note his reaction to having killed her:
Not on purpose. Doesn't seem fair somehow. I mean, we would have both been dead, too, if she hadn't eaten the berries first.
Peeta is a character who therefore remains true to his principals and to his emotions throughout the Games. Even at the beginning, when he makes a rather tenuous treaty with the Career Tributes, he only does this so that he can be in a position to protect Katniss and help her survive, which he does at the cost of his own leg.
Peeta stays true because he has always loved Katniss and made sure to protect her and even when he made a treaty with the other tributes he stayed true to those words, yet at the exact same time he made sure Katniss would stay safe and sound and never became the murderer he could have been.