Tail fin vs stopped blades
It does have a tail fin... but without any rotor speed, it also has four equally-long, flexible, stationary, carbon fibre projections on top, that will probably starkly modify its aerodynamics, especially since soon it probably wasn't going very quickly or at a conventional attitude.
The intermediate moment-of-inertia axis is probably pitch (with roll less, and yaw more), which would be naturally associated with "tumbling" to start if the accident process began with a pitching motion.
The eyewitness effect is also to be considered - is a "tumble" actually a corkscrew, or rotation in yaw? If the rotors were moving, then yaw is the only axis in which rapid motion is possible, and the large angular momentum vector should make it resistant to exciting motion in the other axes.
The dynamics of a helicopter with no rotor speed can probably be investigated accurately with a small-scale model that has an accurate weight distribution, certainly to the point of the onset of a "tumble".
If there was a data recorder or any video, then the speculation could be set aside, but it seems that no photographers have come forward. Even data from an accelerometer or magnetometer on a phone onboard might perhaps be useful.