I haven't read that article in a few years, so it's good to refresh a bit. Figure 5 shows that DOC levels in the aquarium are HIGHER when the skimmer is used, and LOWER when the skimmer is not used. This is because skimmers don't remove (much) DOC, but do remove food particles such as bacteria. Since bacteria are what consumes DOC, the DOC rises because nothing is consuming it:
Also...
I was off by 1%Organic carbon in both its particulate and dissolved forms has been called "the soil of the sea" in recognition of its role at the very foundation of the entire marine ecosystem. It is the sustenance of the microbiota in the oceans and the entire marine food pyramid rests on the availability of this fuel source. Greater than 97% of the organic matter in the oceans is in the form of DOC