Harbor Freight Fuses

Would you not expect problems to start with by using a 15 amp fuse in a 10 amp circuit? Are you sure the owner didn't wrap a wire around a blown fuse? I would never use HF fuses anyway but this seems like it was likely the owners fault too.

The picture isn't clear enough for me to see the actual blades of the fuse and any connectors that may be present.
Isn't the fuse supposed to be rated 33% above what the current will be and 33% under what the wiring will handle or something like that?