First, that isn't what he said. He said they do not break or form chemical bonds. This is patently false, at least if you believe in modern day physics. He also implied earlier that a capacitor contains free electrons... again, false.
Second, no one mentioned anything about changing chemical composition. Obviously the whole reason why batteries work is because one changes the chemical composition.
As I said in the an earlier post, it all has to do with the strength of the bonds. That alone should tell anyone with any basic knowledge of chemistry/physics that there is a difference.
Conductors have a high electron mobility which allows massive amounts of electrons to flow quickly. This is why capacitors can be charged and discharged quickly. Electrons in an atom that is "conductive" has very weak bonds and can easily be removed or added(depending on specific type of atom).
In batteries the atoms carry the charge and electron mobility only occurs at the electrodes. As the chemical reaction takes place the electrons migrate through the electrolyte to cathode then through a conductive path and to the anode of the battery. The migration of atoms are much slower as they are much larger and must travel much larger distances than your typical electron in a capacitor. (It's more complicated than this because the electrolytic solution is full of recombination's)
The goal then is to quick charge and discharge rates like a capacitor and high capacity like a battery. Since you physically cannot put enough electrons on a cap of any practical size to contain as much energy as a standard battery(See the other post about a "pound" of electrons) the approach would be to reduce the distances having to be traveled by the atoms in a battery.
The nanoscale approach is effectively reducing the anode to cathode distance which increases the charge and discharge rates. We achieve the same thing on the macroscopic scale when we put batteries in series and parallel. If we can shrink this down to the nanoscale then use charge/discharge rates could be realized. The problem with this, just like with capacitors, that the capacity decreases.
If we can design a device that uses the conductivity of capacitors and the capacity of electrolytes then we might get somewhere. e.g., have a conductive channel, on the nanoscale, that can transport the electrons quickly instead of having to transport them through ion mobility(which is much much slower than electron mobility in an electrolyte). In some sense we allow the electrons to "hitch a ride" on the conductor. This maybe what is happening in some of the newer lithium ion designs that use nanowires.