Could improper deplaning of a flight with full fuel tanks cause the plane to tip?
The 737-900ER has (two) auxiliary fuel tanks in the aft cargo compartment, behind the wing (and center of gravity) with ~3400l capacity for increasing range (from 2800nm to 3,200nm). 

In usual conditions, unloading of passengers wouldn't be a problem as the fuel would've been used up; However, as this was an overweight landing with full fuel tanks (the auxiliary fuel tanks weigh ~ 3t), the crew are just being cautious to prevent any incidents.