This is actually a very good question. It can also bring to light other details regarding various definitions and details about (press passes, press credentials, media passes) and the like.
Press passes can be both free or have some sort of fee associated with them either directly or indirectly.
If you are speaking about a press pass or press credential that is issued by the possessors employer, this type of press pass would be issued to the holder in all probability at no charge as they would be using such a credential/identification in the course of their job function(s).
A press pass and or press credential can also be issued by an organization or association (trade group/website). This type of press pass would likely be issued as part of their association membership which usually has a professional fee or membership cost associated with joining.
If you are referring to a press pass, media pass, VIP Pass, venue pass, backstage pass, this type of credential is typically issued for free by (venue management, managers, artist management, PR) or other individual or group that is in charge of the venue or event. This issuance of this type of media pass is usually dependent upon the individual requesting the pass having a pre-existing press pass or media credential. It is the possession of a press pass, media pass that lets the individual or group that issues event type passes know that the inquiring individual has some establishment of a role in media/new media.
The US Press Association "USPA" issues a press pass to it's members as part of it's proprietary industry membership packet. USPA credentials and press pass are issued to a member regardless of the membership packet an individual chooses.