Sorry but classic PRC!! Been there before.
PRC is not yet WGS-84, therefore the BS NDB is required (as previously stated) and if it is u/s then you were correct to ask for a different solution.
Practically however the FMS will fly the plane more than adequately and if you want to depart then this is what you will have to do.....as will the 'local' operators!
Some Jepp charts have MSAs based on NDBs so the only way to get the 25DME is to use the FMS progress page (or similar). Khaosiung in Taiwan is an example of this. If your ops manual does not specify that substitution is acceptable with Navaid outages or for MSA calculations, then you must ask for radar guidance. Would also actually need to confirm with PRC AIP that ZHCC is approved for radar vectors before accepting. Not all PRC airports are so approved...radar monitoring but not vectoring...beware! Possibly why they were reluctant.
Furthermore since you would be above the MSA by DUMAG terrain clearance would not be an issue and direct WXI would also be a practical solution.