Getting in touch with your contact persons before you submit your application to PMI is a best practice that should ensure that you pass a possible (but usually unlikely) audit with flying colors. You want to make sure that your contact persons agree with the numbers and information you provide on the application.
And you are correct that the "package" that PMI provides during an audit will contain the same information. However, this package now has to be printed, physically signed by your contact person and then placed into an envelope by your contact person and this envelope has to be sealed across the flap on the back. Now it goes back to PMI for review and inclusion in the audit information.
The idea of sending your numbers to the contact persons first is to ensure that they have already seen and agree to the information on your application ahead of time. In this way, there will be no problem for you during the audit.
In all the time that I've been teaching for the PMP exam I only heard of 1 student who failed their audit because his contact person disagreed with the numbers. I want to make sure that you are not the second one.