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.")
Electrons are flowing from negative to positive when there is a connection for them to flow. You can also think of it as "holes" (or the absence of electrons in an atom) flowing from positive to negative.
Because of historic reasons, we generally think of conventional current, or the "holes", rather than the actual electron current. You are correct that the positive terminal just "pulls negatively charged electrons."
There is also no magical node called "ground." We simply assign a point that is easy to keep track of to refer to as ground. In a circuit, you could refer to the positive terminal of the battery as ground, and simply be working with negative voltages (though it would likely cause some confusion for others interpreting your work).
Likely in the case of shorting the battery to the chassis of the car, the negative terminal of the battery is already connected to the chassis. Possibly this is done for some sort of EM shielding (vehicles are inherently very noisy environments). When you make another connection from the negative terminal of the battery to the chassis, no current flows. When you connect the positive terminal, current flows through the chassis of the vehicle to the negative terminal.
Best Answer
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).