The candidate might seem very trustworthy, but to ease your mind and to fully justify hiring this person, take the time to check both the professional and personal references. Think about it, if they are lying about their references, you never know what else they might be lying about. In many cases HR will perform a background check, which will help as well. You want to be assured that the person you hire can do the job, contribute to your growth and development, and have no past history of violence that might one day endanger your employees.
Also keep in mind that you might be liable if you failed to do a background check on a person who then attacked another in your workplace. That alone should give you reason to not ignore this important part of the hiring process.
Many companies you call will only verify the employment dates and not job performance. At least you will know they did indeed work at the location they stated, and at the same timeframe that was stated on the application.