A trusted intermediary is a central party that both sides rely on to complete a transaction, so they never deal with each other's accounts directly. In the proximity method, the routing server is that intermediary.
The longer version
A trusted intermediary sits between two parties and handles the sensitive exchange on their behalf. Each party has a relationship with the intermediary, not with the other side. This is a familiar pattern in payments, where a processor or bank stands in the middle.
In the proximity method the central server is the trusted intermediary. It holds the registrations for payer and recipient, records which two are paired by presence, and routes the transaction between them. Neither device needs the other's account details.
The intermediary also anchors control and privacy. Because everything passes through one accountable party, the rules about what is shared and when can live in one place, and nothing moves until the payer chooses to act.
The Parousya method
The trusted intermediary is the server at the heart of the Parousya method. It routes every transaction between registered parties, which is exactly why the devices never connect directly to each other.