The aircraft is commuter category, and the performance graphs in the FMS refer to FAR 23.67 (e) and 23.77 (c). From the FMS "The landing gear was retracted as soon as aircraft had left ground and positive climb rate established. Primary controls were used to control direction and wings level attitude after take-off. Trim and engine power settings were not changed during this phase."
At gross weight at sea level the TODR charts provide a take off distance to 35' on a runway with 1% up slope at temperatures significantly warmer than the first segment chart shows a zero climb gradient. The only way I can see this as being possible is with the assistance of a significant amount of ground affect with the flight path possibly even paralleling the runway at quite a low level until the undercarriage retraction is complete. I appreciate that it is difficult to quantify the amount of benefit gained - I certainly didn't expect it too be as much as the number I came up with.
Unfortunately the AFM is not the ultimate defense. If a pilot believes the performance data is optimistic garbage but relies on it anyway, and a crash proves this to be true, the courts are likely to treat this as reckless.