evidence? as far I can remember they have no formal currency, and use caps simply as mean to trade and deal with the outside world.
He's probably confused. The Institute doesn't trade with members of the Institute (with the exception of the Lone Survivor).
Food and Water is rationed out, not sold. Uniforms are provided. Members make requests for tools to do their jobs. They don't have need to buy anything.
The requisition kiosk is for synths and members to request tools and weapons to complete their work above and below ground. These items are returned for upkeep when finished with.
The requisition kiosk has a supply of bottle caps aquired by synths going out and trading as part of their missions.
Synths can request caps for their missions.
The Lone Survivor is given permission to exchange caps and equipment with the Institute.
The Institute has no currency. They only keep caps because they have worth to wastelanders.
