Depending on the placement of the sill plate and the construction of the basement, the FHA inspector most likely is correct in his statement, assuming the type of cable you’re using is nometallic-sheath cable(romex). The odd item is the inspector couldn’t point out in the code where this is required. This is covered in the 2011 National Electrical Code, Article 334.15(C)(Exposed work, In Unfinished Basements and Crawl Spaces). The NEC makes it clear that physical protection is always to be provided where the cable is subject to physical damage, which is a possibility in an unfinished basement. The article is used to define how the cable can be used in exposed work. The important sentence in this article states “Nonmetallic-shealth cable installed on the wall of an unfinished basement shall be permitted to be installed in a listed conduit tubing or shall be protected in accordance with 300.4.
A photo of the installation would help out in making a final evaluation.