I don't like to waste thread space by providing multiple answers to essentially the same question, so here goes:...
...Every citizen, including public officials right on up to the President has a "right to privacy." The "freedom of the Press" refers to their right to seek information and to publish it.
But it is not an absolute right, otherwise in their quest for information to report, they would be allowed to invade your home, private office, or any other private property or restricted government property. They could hack your computers, demand access to your safe deposit boxes, etc. However, we know they can't do this, again because of that pesky "right to privacy."
The Press cannot compel you to speak to them, because you have a right to remain silent. When it comes to criminal law, this right is fairly specific. i.e. you have the right against self-incrimination and you have to invoke it. But in every other day-to-day endeavor you don't have to speak to anyone unless it is a function of your employment (i.e. customer service, receptionist, etc.). Even then, only if you wish to keep that employment.
Now when it is an essential function of government service, it still only applies to your actual duties, and it appends to those whom you must engage with in the performance of those duties. It is not the duty of the average government official, elected or otherwise (aside from those specifically assigned public relations duties), to speak to members of the Press.
The President was not elected to serve the needs of the Press. There are no such duties enumerated in the U.S. Constitution. While he is a public figure, and thus subject to public scrutiny, he still retains all the rights of any common citizen. The White House is his residence while in office, and while it is a public building it's access is restricted to those allowed to serve at the Presidents pleasure, those assigned to his protection, and those hired to provide building/residential services. NO ONE can just walk in without permission, and like any other resident, the President can decide who has such permission at any point in time.
IMO it is a good idea for any President to be as transparent as possible within his privacy rights, but he has no specific obligation to do so, nor do we as common citizens.
Meanwhile, as already stated, lack of access to the President, just like that same lack of access to YOU the common citizen, does not prevent the Press from publishing whatever newsworthy item their hearts desire, subject of course to appropriate Libel and Slander restrictions.