I said the first 500 non-towing miles. I know there is some towing break in, and I did not disagree on that part. But to be complete, here is the towing break in from the manual. And it does mention more than the trans and running gears:
Do not tow a trailer at all during the first 500 miles
(805 km) the new vehicle is driven. The engine,
axle or other parts could be damaged.
Then, during the first 500 miles (805 km) that
a trailer is towed, do not drive over 50 mph
(80 km/h) and do not make starts at full
throttle. This helps the engine and other parts
of the vehicle wear in at the heavier loads.