I really think it varies depending on the personality of the child. I know children who are very straightforward, literal, rules-oriented, or justice (fairness) oriented, who really don't lie.
My older son, who is introverted, quiet, loving, and a serious conflict-avoider (absolutely could not handle to disappoint or be spoken to harshly, or make eye contact when you say "I love you," or have a "feelings" talk), lied a bit at that age. He denied wrongdoing to prevent trouble or conflict (and we are very gentle responders). We communicated that it is more important to be honest and that we wouldn't punish him, but that was unbearable for him, he'd deny hiding the truth and climb under his bed. He got braver and more clear that it is important to be truthful, and at seven he handles things much better. But I am willing to bet that due to his personality, his first instinct may always be to conceal rather than admit to something problematic.
My younger son, on the other hand, admits wrongdoing very clearly, and even when you downplay it ("you didn't mean to"), he restates it, ("but I did get marker on the couch, I did, I got the marker on it!") He's much more naturally truthful and direct. He sometimes "exaggerates" but I don't see that as lying cause he actually believes what he is saying. He sees the world in dramatic terms and expresses it as such. And if you call him on it "a hundred pieces? really?", he'll usually modify with a laugh.
Personality types really make children different from each other and I don't think either is more "natural" for a 3 year old. They are just different people and teaching about reality v. fantasy, bravery, truth, taking responsibility, etc... is going to take different forms with different kids.