One of the most important things a landlord does is select tenants. Make a mistake and all the work you just completed and money you spent could all be wasted on a professional tenant that has no intention of paying their rent. Or it could be wasted on a person with good intentions but the inability to keep paying rent over a long period of time.
Managing rentals is not sales. We have to live with our mistakes day in day out. That is if we are lucky. If the mistake is bad enough, we might lose a client or spend a lot of time, effort, and money cleaning up the mess that was created.
My office decided a long time ago that our best bet was to check our own tenants out. We run our own credit reports using one of the major credit agencies. Then we ourselves call the landlords and employers to verify rental and job history. Many companies use 3rd party vendors to do this. The problem is that these 3rd party vendors many not be employing the old school methods we use. I know this because a tenant we were kicking out for very poor housekeeping habits was recently rented to by one of those 3rd party vendors that is supposed to be calling past landlords. We never got the call!
A couple of methods we employ are to use a reverse phone book (also available online) to find out who owns the phones numbers we have been provided by the tenant. We also use the tax records to get the names of the landlord on the deed for past property they rented to make sure the name matches the number on the reverse phone directory. I think many professional tenants are now using cell phones of friends for their landlord references. Do not trust the numbers you have been provided!
The tenant's credit report (make sure you see their social security card and know how to verify that it is real) will have past addresses on it that should match the information provided on your application. If not, start researching until you are satisfied.
In the landlord business it is better to be safe than sorry.

Great information, Robert. It's scary how easy it is to fake references. Kim/AAOA