There is a difference between highlighting the positive contributions you made in your last jobs and lying to the interviewer. It is rare for a company to not conduct reference check these days so don’t say anything that can not be verified by your boss or other references that you provide.
There are many ways to get into trouble during an interview and lying is the most severe. It is better to give a less glossy truthful answer such as I was a member of a team that lying and saying you were the team manager. Likewise do not make false claims about your education (avoid doing this on your resume as well). Remember that you previous supervisor is not going to lie for you. And never take credit for a project or duties which were completed by someone else. This is not to say that you downplay your contributions, experiences or education. You should convey them in the best light possible.
Explain the part you played in bringing a project to completion and show that you were a valuable part of the team. This may not seem as glamorous as being the lead in the project but you are building a strong foundation. An employee that can recognize and share in the success in others is preferable to one who doesn’t tell the truth or wants all of the credit for his or herself.
Honesty is important but you are not required to be so honest that you hurt your chances at getting the job. You are not required to incriminate yourself. Honesty is a job interview simply means not claiming anything that is not true.
What is the key reason people lie in a job interview? It is because they lied on their resume and now they are forced to continuing lying to back up the resume. Keep your resume honest and that will help you keep the interview honest.