Not true. If the aircraft was flying using a basic autopilot such as the STEC 55x, set on HDG & VS mode, climbing with, say, 700fpm, eventually the autopilot will pull the aircraft into a stall as the engine can no longer generate the power required to sustain the climb, the higher it climbs. In order to keep the commanded climb rate, the autopilot raises the nose in order to continue to climb....hey presto - stall. Depending on the VS set, depends how soon the aircraft will stall - with VS+1000 fpm commanded, it will stall much earlier than, say, VS +300fpm.
However for this to develop into a spin, yaw would have to be present in some form or other, otherwise the nose would just drop and the plane would mush downwards. Stalling a Cirrus with no yaw is relatively benign; because of the cuffed design of the wing, the inboard portion of it stalls first, allowing the outboard area to remain unstalled, meaning the ailerons are still effective; in a Cirrus, you can actually use the ailerons in a stall to keep the wings level.... yes, you're descending rapidly but without yaw, it won't spin - the Cirrus SR2x aircraft were considered the first spin resistant aircraft EASA certified.. External factors such as turbulence might create the yaw required to induce the spin, though....
Look at the graph with the green and yellow.
It looks like the autopilot tried hard once to stall unsuccessfully, then a minute or two later it tried again... successfully. Did it get away with a nose drop the first time, then nose drop and spin the second time? As you say, turbulence could cause that, however do you think that a full or cruise power stall with full back-stick may result in a wing drop into a stall with limited yaw input?