Using Ansel Adam's Zone System is helpful when thinking about exposure.
The camera's reflective light meter is not giving you an incorrect reading.
Look at Ansel's
Zone Scale ...
Now ... let's say we take the camera's reflective light meter and look at the black bag.
The camera says to set your camera at 1/4s @ f8.0 (the camera's exposure scale is at 0).
The Zone Scale says that the exposure is in Zone V (middle grey).
You know that the black bag should be darker than that. Looking at the Zone Scale you figure it should be in Zone III.
In order to render the bag in Zone III you need to shift the exposure down by 2 stops.
To lower your exposure you can either increase your shutter speed (1/16s) or increase your aperture (f16).
Now, you ask what happens to the other objects in the shot ?
If you have properly placed the black bag in the right Zone then the other objects should also be in a matching Zone.
Sometimes that is not the case ... some scenes include objects at extreme ends.
If you take a meter reading of the dark object and the light object they should be within 8 Zones of each other.
ie black object (Zone I) = 1/4s@f8 and white object (Zone IX) = 1/500s@f8
If it is greater than one of the two will be rendered outside the useful Zones (Ansel was shooting film so he based his Zones on that) ... causing under or over exposure.