Would an employee tell honestly why he would leave his current job? How would you know if an employee is telling the truth on why he is leaving?

Many people are honest about it, but many are not.  There is no way of telling.

Reasons for giving false reasons are most commonly social. If you leave because you hate your boss, and your boss asks you why you are leaving, very few people will give the real reason.  Sometimes the real reason is confidential or family-based.  In order to try and circumvent this problem, many large companies use an exit interview conducted by HR.  This does give slightly better results, because it's easier to be truthful.  Sometimes a written questionnaire is used.  I presume (although I don't actually know) that some companies use an external HR consultancy to create even more distance, in order to help the ex-employee to be honest.

However, why somebody leaves is their business and they are under no legal or moral obligation to give a reason.  If you are asking the reason, you are asking a favour.