Are we allowed to know what kind of oscilloscope it is? Make and model number?
Regardless of that, your symptom may point to the transformer (as the troubleshooting flowchart says.) The filament of the CRT is elevated to high voltage, and this can leak through the filament winding into the rest of the transformer and cause the unit to draw more current than it should, blowing the fuse.
You can check this by powering the CRT filament by an external transformer instead of the scope's transformer, being aware and careful of the HV elevation. If the scope works and doesn't blow the fuse, you can then permanently install the extra filament transformer inside the case, thus keeping the HV out of the main transformer.