The possesive can be used for anything, not just living things (I've heard of others who have been taught the same rule as you, I'd be interested in where it came from, as it certainly isn't correct). 'Statue's torso' is fine. As are 'the book's cover, the plate's pattern, the car's engine, the building's roof, the cupboard's shelf, the train's wheels', etc etc etc.
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Nona the BritThe possesive can be used for anything, not just living things ... If something belongs to something else - even in the sense of being part of the whole - then use the possessive.
How about 'anniversary's celebration'?
Regards,
Slava