What do you think?
A possibly related hint: consider the miscibility of alcohols of varying lengths in water.

That’s a pretty general statement about protein structure, and it’s true as far as it goes. Not all hydrophobic side chains are buried, and not all charged residues are on the surface—though most of the latter are solvent-accessible. But the distribution of polar/non-polar residues isn’t the only determinant of solubility. And then there’s also the question of how soluble is soluble? The real “determinant”—so far as solubility in simple aqueous buffers is concerned—is how well water can solvate the protein molecule, and this is a function of salt, pH, temperature, concentration and other miscellaneous factors. Polar or charged side chains on the surface solvate pretty well, but there are plenty of non-polar exposed side chains in the average protein, too. These may or may not adversely affect solubility. Exposed non-polar residues mostly affect the entropy of solvation by “freezing” water molecules in the vicinity of the side chain as an attempt to present a more polar suface to the solution—although the importance of this effect has been called into question. Hydrophobic patches of residues on the surface can lead to aggregation which also tends to reduce solubility. Denaturation also plays a role: in general, denatured proteins are less soluble that properly folded ones (there are exceptions, but they are rare), so anything in solution that might promote denaturation will (probably) reduce the solubility. What I’m saying is that solubility is a balancing act between favorable/unfavorable thermodynamic factors, of which the distribution of polar/non-polar residues is only one of many.

I should have pointed out one thing that might, at first, seem like a contradiction. I said that denatured proteins are, in general, less soluble than properly folded ones. "But then why does urea or guanidine hydrochloride solubilize proteins; don’t they also denature them?" Yes, they do, but the dissolution of urea or guanidineHCL in water, though it is a spontaneous process (deltaG < 0), there is a negative entropy contribution as these molecules tend to strongly order water molecules in their vicinity. You get some of this entropy back when urea gives up its bound water to interact with the protein and then both the enthalpy and the entropy of the reaction (to be denatured and go into solution) are favorable. So it really is consistent-it just looks inconsistent at first blush.