While your reasonin might have a certain sense of logic to it, 10CS, the definitions of time intervals (whether they be seconds, minutes, hours, days, months, years, decades, millennia or whatever are all man-made. When people refer to the '1920s', 1960s' or whatever, most other people would assume that they're including '1920', '1960' or whatever within those decades.
For example, people listening to 'Sounds of the Seventies' on Radio 2 expect Johnnie Walker to include music which was released between 1 January 1970 and 31 December 1979. There would probably be complaints if he refused to play Elvis Presley's 'The Wonder of You' (released in 1970) because he'd followed your logic and assigned it to the previous decade.