There is a difference between telling a story highlighting the positive to make you sound better 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.
Common fibs that are told include educational degrees that you do not hold, saying that
you are a manager when really you are a team lead and taking credit for a project that was
completed by a coworker. All of these things can make you sound good at the time of the
interview, but what if the interviewer talks to your boss about the stellar project you ran
for the company when it really wasn’t you. Your boss is not going to lie for you and if
you were in the running for the job, you won’t be anymore.
The best way to handle these scenarios is to tell the truth but put you in the best light.
Maybe you were a part of the project, instead tell the interviewer the part you played and
share the success of the project as a whole. 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 themselves.
This does not mean that you have to share all anything that doesn’t put you in a positive
position though. The key is to be honest and only bring up examples that are going to
highlight your talents and work history in the best possible way. Don’t claim or state
anything that cannot be backed up by your references.