1. When people asked Peter if he was a manager, he stretched the truth by telling them that he managed the office where he worked. What he didn’t tell them was that he was the only person in his office and he only managed himself.
2. Sometimes when people apply for a job, they stretch the truth about what they did in their previous jobs in order to make themselves seem more important or more desirable.

Compare to: white lie. The expression suggests that one can distort or bend the truth, so that others are misled, without actually telling a lie.