Despite the fact the our voices do sound different, wether or not we are pitch perfect is more the issue and how it was determined that the singing was 'good or bad'.
I know that I prefer my speaking voice in my head, when I'm being my lazy vocal self, than my speaking voice recorded.
If I'm doing voiceover work or singing though, I have a better time controlling what my tone is, and how I sound.
I can make it sound more like the vocal sound that i hear if I am aiming for it while recording. It's not exactly the same but it is damn close.
Generally, though, the recording is not a task for me to see if I can make it sound like it does in my head, it doesn't matter at all, getting the tone, pitch, inflection and emotion are really way more important, I think.
Despite Edison, there are plenty of people who really shouldn't be singing at all, that still do! And they believe that they are AMAZING! Just tune into American Idol auditions coming up for further proof of that!