The confusion here is from the initial poor description of how a battery works.
A battery consists of three things: a positive electrode, a negative electrode, and an electrolyte in between. The electrodes are made of materials that strongly want to react with each other; they are kept apart by the electrolyte.
The electrolyte acts like a filter that blocks the flow of electrons, but allows ions (positively charged atoms from the electrodes) to pass through. If the battery is not connected to anything, the chemical force is pulling on the ions, trying to draw them across the electrolyte to complete the reaction, but this is balanced by the electrostatic force-- the voltage between the electrodes. Remember-- a voltage between two points means there is an electric field between those points which pushes charged particles in one direction.
When you add a wire between the ends of the batteries, electrons can pass through the wire, driven by the voltage. This reduces the electrostatic force, so ions can pass through the electrolyte. As the battery is discharged, ions move from one electrode to the other, and the chemical reaction proceeds until one of the electrodes is used up.
Thinking about two batteries next to each other, linked by one wire-- there is no voltage between the two batteries, so there is no force to drive electrons. In each battery, the electrostatic force balances the chemical force, and the battery stays at steady state.
(I kind of glossed over what it means for two materials to "want" to react with each other. Google "Gibbs free energy" for more details on that. You might also google "Nernst equation.")
It sounds from your question that you aren't asking about the effects of electron flow in the "wrong" direction on battery chemistry, but rather asking if a "positive" voltage can "act like" a negative or a ground. If so, then the answer is yes, it can.
All voltage is relative, so your reasoning is correct. If you connect two positive but non-equal voltage nodes together, current will flow between them.
Calling something "positive" only means that it has a higher voltage potential than something else which you are using as a ground reference.
You can think of it as pressurized cans of air. Let's call 1 atm (which is air pressure at sea level) our reference pressure. If you pressurize one can to a pressure of, let's say, 2 atm, you might say it has a "positive pressure". If you then pressurize another can to 3 atm, it also has a positive pressure. Connecting either can to a 1 atm pressure (i.e. by opening it) will cause air to flow out of it (this is analogous to electrons flowing in the wire) until the pressure equalizes. But if you connect the two cans to each other, air will flow out of the 3 atm can and into the 2 atm can until the pressure equalizes.
So it is with voltages. The electroncs that are under more "pressure" (voltage) will push harder against the ones that are under less pressure (but still "positive", vs. some arbitrary reference).
Best Answer
More apt chemistry term to be taken into account is standard reduction potential. Not electronegativity. It's a measure of ability of an atom to get reduced i.e., gain an electron. The electrode with more reduction potential is taken as cathode, where reduction takes place. And the electrode with lesser reduction potential is taken as anode, where oxidation takes place. In a battery, both reduction and oxidation reactions takes place simultaneously to produce current through the external circuit (known as Half reactions, and together known as Redox Reaction). So that at anode electrons are generated , and at cathode these electrons are gained. The difference between the reduction potentials of cathode and anode makes up the cell potential or voltage of the battery. This is responsible for the electric field from cathode/positive to anode/negative of the battery.