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They probably are all connected.
A common pcb practice is to connect all the grounds to one point on the board, to combat ground hum and other issues.
High currents going out to the speaker returning on the common line (assuming its not a brdged amp) would cause the ground to fluctuate a little due to pcb trace resistance, so if you grounded the speaker right at the audio in connector you'd get feedback issues, same applies for power connections etc.
Tha above is a good idea, however the sending device needs a ground!, which can be a seperate cable.
Shields should be connected to Earth at one side only. The side is usually the souring side of the signal.
Home audio violates that rule.