Basically, plants preferentially take up CO2 containing lighter carbon isotopes. When fossil fuels (which, after all, are the remnants of ancient organisms) are burned, the CO2 released reflects that mass distribution and is therefore relatively lighter compared to CO2 coming from non-biologic sources.
But how much CO2 comes from non-biologic sources?
Even limestone (seabed - magma - volcanoes) was originally plants/algea/diatoms deposited on the ocean floor.