Silver most definitely oxidizes. Ask anyone who has solid silver or silver plated items (flatware, wedding gifts such as teapots and serving trays, old native american Indian jewelry, silver coins etc).
Any silver that does not oxidize has been treated in some way to resist this - coated with varnish, plated with an additional metal on top of the silver, or silver mixed with special base alloys (called 'tarnish-resistant silver' in the jewelry business), etc).
The thing I'm not sure of it why it oxidizes to green. Silver oxidizes to black.