I'd guess the fuel is very nearly depleted at landing. This would put the center of mass somewhere fairly low on the stage, close to the engines which are dense, heavy things.
This means that the landed stage isn't as susceptible to toppling as it looks. At minimum, it would have to tilt so far that the CoM went beyond the line connecting the ends of two adjacent landing legs and tilt along a radius that crossed the midpoint of that line. Other tilt vectors would require more tilt to overturn the stage, based on CoM & landing leg geometry.
Wind loads could assist a tipover. The stage is ~12 feet diameter, it's really tall, it presents lots of sail area and it's pretty light at landing. Wind force would be a fun estimation to do.
They both have their "plans" on what to do, and the rocket basically is doing everything from what it can "see". There is no back-and-forth communication happening at all.