Close Giovanni, but not quite. The ICBO certified inspector is technically an employee of the building owner and is under the supervision of the designer. An ICBO SSW (Structural Steel & Welding) inspector is not involved in the planning or design of a building, but is responsible for assuring that work involving the fabrication and erection of structural steel is completed according to the design and any applicable building codes. As an inspector the SSW observes those areas of work whithin his scope of responsibility and reports to the engineer or architect when the work is acceptable or rejected.
ICBO refers to the AWS codes for all welding applications but also refers to the American Institute of Steel Construction (AISC) Steel Construction Manual for other elements of steel frame construction. Another publication by the American Iron & Steel Institute (AISI) is referenced for light weight and sheet steel materials used in cold formed elements.
To qualify for ICBO certification, the inspector must be familiar with AWS D1.1, D1.3, D1.4, the AISC and AISI manuals, be able to read steel framing plans and know when to apply each to a particular case. Because of the broad range of work covered by this classification there may be several SSW inspectors on a single job. Generally among them is a supervising inspector or, as in Los Angeles, the SSW also reports to an inspector representing the city or jurisdiction.
It took me many years to understand all of this. Just as in all trades, it takes experience to grasp all the complexities of the job.