What I'm concerned about is whether or not the Memorex batteries are identical to the Walmart batteries (Initial RB-270). If they are, then I'd agree that it would make sense that a simple 12 V automotive plug to type M (5.5 x 2.1 mm) power plug adapter cable would do the trick. However, if the Memorex batteries use a different charge controller than the Walmart batteries, then it might not be so good an idea. The cigarette lighter adapter cable does not come with the Walmart batteries and I have already built a DIY cable for it. I just don't know whether it's safe to use the cable yet.
On the subject of regulator dropout, that LT1086CT-12 only has a 1.5 V dropout voltage, so that allows delivery of regulated 12 V from a 12 V automotive system whose fully charged voltage ranges between 13.8 Vdc and 14.8 Vdc, depending on whether or not the vehicle is running at the time. When charging the Walmart battery, the AC adapter pulls down a bit to 11.25 V. Taking into account the 1.5 V dropout voltage, that implies that unless your vehicle's battery voltage drops to less than 12.75 Vdc, using the LT1086CT-12 would be no problem.
If you are worried about the dropout voltage taking that voltage too low for the charger to work, then you have to ask about whether the Memorex cable would work on a car battery with a dead cell or that had been run down, trying to start a car.
I guess it comes down to a question as to which is worse, "overvoltaging" the battery's charging port (with unregulated automotive 12V) or undervoltaging it (when your car's battery gets low). Or is either one a problem? I wouldn't even raise the question if the Walmart battery was supplied with a cigarette lighter plug adapter cable.