The Law of Network Gravity states: It is always easier to be bumped down in the organization than it is to be bumped up.
What this means is that if you have been referred to the President of the company, but you realize your potential Hiring Manager is the Accounting Manager, you should still contact the President. It may seem intimidating at first, but if you have a personal referral to use, it typically goes quite smoothly. Let the President know who referred you, the purpose of your call, and ask if they could refer you to the proper person within the company.
That's when the magic starts. Why? Because now you have a referral within the company who is in the reporting order of the Hiring Manager. This is as golden as it gets in a job search.
Let's take the example of seeking an accounting position. The President, not likely to have the name of the specific Hiring Manager, might refer you to the Chief Financial Officer. Onward and downward to the next level below. When you call this person, make sure you state that Mr./Ms. President asked you to call them. Just watch how quickly your call is accepted. The CFO will take the call and will probably refer you to the Controller, who in turn will refer you to the Accounting Manager. At each level, you continue to "layer on" the name dropping from all the previous levels. By the time you get "bumped down" to the Hiring Manager, you can now state that you are calling based on the recommendation of the President, CFO, and Controller. Wow! Watch the results! Interestingly, they usually do not ask why they recommended you talk with them. So it could even go as far as the Hiring Manager wondering if you are in some way related to the President or have some other "insider" connection. Now you have become an insider! Congratulations—make the most of it!
So don't be intimidated if you are given a high-level contact. Instead, treat it as a wonderful gift and spend it wisely.