Physical selectivity in terms of solubility just comes down to the different mass, and 13C-CO2 (45 g/mol) is just 2.2% heavier than 12C-CO2 (44 g/mol). Oxygen isotope selectivity is stronger, since in water we're talking an 11% difference in mass between 16-O and 18-O water. Biological selectivity comes from differences in size and chemical properties between the different carbon isotopes, and outweighs solubility differences 20-50 fold.
Overall, the oceans are actually slightly enriched in 13-C compared to the atmosphere, both since heavy isotopes have higher solubility and biological activity keeps preferentially sequestering the 12-C. So if the extra CO2 appearing in the atmosphere was coming from the oceans, we'd expect to see a very slight increase in atmospheric 13-C rather than the observed decrease. It's true that volcanic emissions are slightly depleted in 13-C relative to the atmosphere - but we'd need to account for at least 5 times more CO2 to get the observed changes compared to the case of fossil fuels as a source.
Seriously, this particular brand of denialist is really perplexing to me. Simple accounting says we burn more than enough fossil fuel to account for the observed CO2 increases, the isotope data matches, and heck - we can even see the change in atmospheric oxygen matching our CO2 production. Occam's razor clearly applies here - but some insist on invoking convoluted fantasies involving 1000-fold increases over known volcanic emissions. Weird.
