I know what you're saying, but you haven't explained how damage can occur.
The reason you can't explain it is because it's just a few more myths touted
by the marketing departments of certain manufacturers.  In fact, there are
some manufacturers that actually *recommend* running two different signals
to your DVC sub - that is, running a signal into one coil and shorting the
other.  Check the Adire Audio website for an example.

Here: I've done the legwork for you.

From the Adire Audio web site:

http://www.adireaudio.com/Files/TechPapers/DualVoiceCoilDrivers.pdf

"There's one thing that often comes up about wiring DVC subs, and that is
the mistaken conclusion that running different signals to each voice coil
will "ruin" the driver. Let's recall how a dual voice coil driver is built.
Basically, a dual voice coil driver consists of two motors (the voice coils)
co-axially mounted (that is, wound together on the former) to a single
diaphragm. The net force on the diaphragm is the sum of the inputs of the
two motors.  Now, when you feed disparate signals to the motors, they do try
to counteract each other. However, this will NOT result in mechanical stress
in the system!
"Why? Well, remember how a dynamic cone driver works. You have a static
magnetic field from the permanent magnet. Then you have a dynamic magnetic
field from the voice coils. It's the interaction of these two fields that
generates the force that moves the voice coils/former that are attached to
the diaphragm. Thus when the voice coil dynamic fields push against the
magnet's static field, you generate a force on the former, which pushes on
the diaphragm, and that pushes on the air, generating your acoustical wave.
Now, when you feed the same signal to both voice coils of the driver, the
dynamic fields of each coil are the same. They add together, and generate
one single force (equal to the sum of the two individual forces) against the
static field. Presto, cone motion.

"Take the "worst case" situation. You wire the two voice coils out of phase.
At first, you think one coil is trying to push forward, the other backward,
and suddenly the system tears itself apart, right? Nope. What happens is
that one coil sets up a dynamic field. Let's say, for clarification, that
coil 1 generates a signal to push the diaphragm forward. Since coil 2 is
wired in opposite phase, it sets up a dynamic field to push the diaphragm
backward. Net result is that the two magnetic fields CANCEL themselves out!
That is, the dynamic field that's pushing on the static field from the
magnets is ZERO. The field from coil 2 adds to the field of coil 1 in such a
way that the net field is zero. Much like adding a two sine waves of the
same frequency that are shifted by 180 degrees."

"This is the SAME basic principle with shielded drivers that use bucking
magnets. Use a field of the opposite polarity to cancel the original field
out. If the driver's motor magnet has a given polarity, use the bucking
magnet to introduce a field of opposite polarity, so that the two fields
cancel themselves out. Net result is no field. So, when we run two different
signals to the voice coils, what we find is that the magnetic fields of the
two combine to generate a net TOTAL field that interacts with the static
field of the magnets. The two voice coils NEVER fight each other in a
physical way; it's all in the magnetic field."

So which manufacturer are you going to believe?  The one that provides an
explanation or the one that simply says "don't do it, or else!"