I think experimentally magnet is not necessary for electrical charges to emerge and natural magnets don’t require electricity to have magnetic properties. They have a big overlap and affect each other but aren’t inseparable. 

 Ok well I think you’re wrong but that’s fine

How else would it be possible…? Magnetism is intrinsic to all things? No? Dia Para Ferro 

 It just may not be noticeable at a scale that matters to humans