Many people tow automatic transmission cars (including older Accord with 4 speed overdrive auto) despite the manufacturer's "yes" or "no" recommendations.
If it is out of warranty, you manage the risks yourself. If you break it, you fix it on your own dime.
Hondas of that vintage were once considered towable. Honda got hit real hard on an "implied warranty" class action with respect to the transmission used in the Accord (and several other cars). After that settlement, the towing policies changed.
I just recently set up my manual transmission Honda Fit for towing. I bought the Fit for that purpose, and because it is a nice size for single guy road trips, around town use, and airport runs to pick up 2-3 people. The automatic is also towable, per Honda's recommendation. The only other Honda recommended towable automatic, since about 2007, has been the CR-V.
Automatic transmission lubrication is not the only towability issue, as much as we'd like to pretend. Manufacturers recommend against towing certain car models based on experience with other types of damage, such as front suspension and frame components in unit bodies, despite the best efforts of towing equipment manufacturers to design towing attachments. Many unit body cars are simply not up to the task, there is no place to attach towing equipment that won't do damage when towing conditions get extreme.
Tom Test
Itasca Spirit 29B