The amount of CO2 released by human activity is measurable...
...by looking at the carbon isotope ratios, which are different from carbon released from geologically sequestered coal beds, oil fields, etc. So while the physics of radiative transfer and the greenhouse effect does not change depending on the source of the atmospheric carbon, the source of that carbon is traceable through a combination of pretty good record keeping and carbon isotope ratios. Both indicate that the amounts released through human activity are enough to trigger the climate changes we are experiencing and that the data is showing us.