I think you misread that anl.gov answer. some factors would increase the amount of CO2 in the water and aothers would reduce it's solubility.
Increase in partial pressure of Co2 in the atmosphere (ie, Co2 concentrations in the atmosphere increase), then yes, this would allow more CO2 in the ocean water.
However, it's offset by some other factosrs (called out in your link above).
1. If the ocean is abosrbing more CO2, it's PH would be decreasing, this would make it less and less likely to absorb additional CO2 from the atmosphere as it reaches a new quilibrium.
2. temperature: if ocean temperattures are rising, the seawater will be able to absorb and hold less CO2 from the atmosphere
These all work together to find the conecntration of CO2 at equilibrium. If the temperature changes, or the conenctration of CO2 in the atmospher changes, then the amount of CO2, the PH and the temperature will also change to adpt to the new partial pressure of CO2.
Regarding your initial statement about sugar in hot water: gases behave in the opposite way that solids due WRT soluability in water. For example, if all esle were equal, a warm coke could dissovle more sugar, but would be "flat" (lacking in CO2 bubles).