The idea that vampires have no reflections, and that they fear crosses, are both traditional ideas held for centuries. In Bram Stoker's Dracula, a famous passage recounts Jonathan Harker's realisation that Count Dracula is not reflected in his mirror:
"Suddenly I felt a hand upon my shoulder [...] and I started, for it amazed me that I had not seen him , since the reflection of the glass covered the whole room behind me." p26.
Stoker's vampires also cower back from crosses and garlic. Rice does not allow any of these traditional ideas to affect her vampires.
Stephenie Meyer takes the heresy even further: Twilight vampires are quite happy in sunlight.