The purpose of the fuses in the upstream panel is to protect the conductors from that point to the remote panel. They do not provide protection for anything inside the remote panel. So the question boils down to whether there is anything inside the remote panel that requires overcurrent protection. If, for example, there is a control transformer and a main line contactor, I think they will need overcurrent protection. That is, I believe, the purpose of having fuses in a motor starter.
As to specific NEC requirements, there is just the general rule that everything must be protected against overcurrent in some fashion. That statement appears in 240.3.
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