Question:why Is The As350 Not Certified For Class C External Loads

[Freewheel]

Latest revision to Cargo hook Swing and Sling Supplements, released in 2020:

"The cargo hook system meets the external load certification regulations for Non Human External Cargo (NHEC)."

Well I guess that clears that up. 5 years later a pilot can reference the Flight Manual and safely answer the original posters question.

The answer to the original posters question. The AS350 IS certified for Class C loads. 

Revised From:

"The cargo hook system is approved for lifting external load which is jettisonable and lifted free of land or water during rotorcraft operation.

Operation with an external load which remains in contact with land,water or any fixed structure is not demonstrated by the manufacturer. These operations shall not be conducted without approval from the responsible authority in accordance with the applicable operational regulations .
The external loads are limited to Non Human External Cargo (NHEC)only."

Which was previously revised from:

"Class of approved aircraft/load combination: B, "Single point suspension, external load airborne". This means carriage of external loads, which are jettisonable and lifted free of land or water during rotorcraft operations. 
The external loads are limited to non human loads only."