I think Peeta comes off as perfect because the book is narrated by Katniss

This is dead on. I don't think we're supposed to view Katniss as a reliable narrator - she's a young girl going through hell, not an outside, analytical voice. It's like when people say Prim is sue-ish because she's so perfect. But she's not really perfect, she's just a sweet little girl whose older sister thinks she's perfect. It's part of the reason that I dislike the first person narrative in the later books; we miss out on a lot of nuance by seeing things only through Katniss' point of view.