They don't need tokens.  The bitcoin network needs tokens in order to pay the miners, who are anonymous and scattered all over the world.  In a "permissioned ledger" (i.e., a distributed mirrored decentralized tamper-resistant database for a closed set of non-anonymous, legally bound entities), transaction processing would be done by the member entities, for whom the service would be compensation enough; and/or by external contractors, who would get paid in dollars through banks, the old-fashioned way.

Thus a "permissioned ledger" does not need tokens or proof-of-work.  It remaisn to be seen whether it will have a use for any of the other distinctive features of the Bitcoin protocol.