I agree and disagree.
That is, plants actually don't absorb "organic chemicals", either. They mostly absorb inorganic ions (ions carry a charge, + or -), which may or may not have been derived from organic compounds. Whether the ions were derived from organic compounds doesn't really matter to the plant (but it certainly matters to the soil).
However, there are synthetic chelating agents to consider, which are prevalent in hydroponics fertilizer. EDTA for instance is synthesized from ethylenediamine, formaldehyde and sodium cyanide (nasty precursors) and forms complexes/salts with minerals (like iron) making them more soluble and forcing their absorption by plant roots. The big question is whether the EDTA is actually absorbed by the plant, and whether it remains in plant tissues after harvesting. Some studies have demonstrated that most of the EDTA remains in the substrate; it releases its mineral counterpart and then it can go form another complex. Other research has found some EDTA in plant tissues.
Either way it isn't great. EDTA likes heavy metals (mercury, lead) and can shuttle those into plant roots as well. So if EDTA released its metal to the plant and then was free to join another complex, it would prefer to do so with a heavy metal. Absorption of other elements like aluminum can be influence by certain factors also, and even minerals that are required by the plant are much less 'safe'/'unhealthy' when present in abundance.