The combined load of branches on a power strip may be capable of exceeding the upstream input protection. There is a fundamental misunderstanding of the purpose of the power strip internal fuse protection. The fuses are not there to keep the upstream breaker from tripping. Circuit protection within the power strip is there to protect the outlets and wiring to the outlets. Thus, a power strip may be protecting the branch outlets at 20A per NEC allowance while the upstream breaker is protecting the wiring and under-floor receptacle.
An administrator should only allow knowledgeable personnel to plug in equipment to prevent circuit faults as well as to keep the current draw under the NEC continuous current safety rating of the circuits.