The only reason I would think polarity might not matter in this case is because if it accepts AC by default then it is already accepting both polarities in a sense. I don't totally get why DC would work in this case, but I suspect the fact that it does work means it is being rectified(?) properly somewhere. Again, this is a hunch, I wouldn't bet my life (or a peda!) on it without more info.
I'm certainly no expert, but my thinking was that at some point the DL4 is turning that AC to DC, which your link and other Google investigations of its power structure have noted. If you were to bypass the AC-to-DC conversion process and tap into the DC part of the circuit, then the polarity is going to matter. It's been a while, but I was looking at all the mods you can have done to a DL4 and I noted some mods made use of the battery compartments space (so no more battery capability) – it runs on C-cells, not 9V or Double-As. Whatever type of battery isn't important, what matters is that all batteries have a positive end and negative end (or terminal). I noted that at some point the pedal knocks the AC down to 6vDC, and I was wanting to tap that to power a small booster or OD to be secreted into the battery compartment.
I don't know if you can plug a 9V adapter into the AC jack on the back and the AC->DC converter ignores or is ignored, or maybe you need to tap 9V into the power circuitry after the converter... Like I said, I'm not an expert, not even really very savvy at all about these things – but I am learning a lot as I go.
So while AC "accepts" either polarity, once converted to DC it then becomes polarity-specific.
I should revisit my Aphex Bass Xciter and Punch Factory. Those pedals are unlike anything I've encountered power-wise. According to the manual you can run them on just about anything any ol' how:
"e. External Power
When external power is used, the internal battery
becomes disconnected and will not experience a
power drain. A wide range of both a.c. and d.c.
supply voltages is acceptable for power (see speci-
fications) and it does not matter whether the center
pin is positive or negative. Almost any existing foot
pedal or stomp box power unit will work as long as
the plug fits the jack. The power jack fits a standard
6MM x 2MM power plug as used by most
popular stomp boxes.
f. Phantom Power
With all pedals built after February 2004,
phantom power applied to the D.I. will supply
reliable power. Do NOT operate the ground lift
switch when running on phantom power. It makes
a horrendous click like plugging in a mic!
g. 9V Battery
You can use any type of 9V battery that fits the snap
connector. You can use rechargables, but the Aphex
unit does not supply a charging circuit. You must
remove the discharged battery to recharge it with
an external charger. We recommend using long life
alkalines. The internal battery is replaced by remov-
ing 4 screws holding the bottom cover. You can
expect from 100 to 150 hours of continuous use from
a fresh alkaline battery. Useful life is ended when the
battery voltage drops below 5.5 volts.
To extend battery life, always unplug the input
when the unit is not in use.
SPECIFICATIONS
5-32VAC
7-48 VDC
+48V Phantom"
That's pretty amazing to me, the power specs: 9v battery, phantom power, AC or DC with centre-negative or centre-positive pin...
If this pedal can operate on any of all that, it's always made me wonder why other pedals can't!