I'm skeptical that the brain could be this delicate in operation and still work as robustly as it does.

States of molecules are in no way delicate. There's points plotted on a line:

delicate----------------not so delicate------------robust--------------------will withstand solvent replacement or brine.

The molecules that unravel and change their shapes (and detach, and lose state information) upon the changes involved would never (for any practical meaning of never) change their shape in such ways in normal conditions. It is not delicate - it is just that changes in the properties of solvents are very non delicate kind of change at all.