i had no idea of its supposed devilish leanings! dont most ambigrams have a 180º symmetric rotation? black metal logos i see tend to have a lefttoright mirror reversal symmetry which arabic calligraphy has used hundreds of years ago!
yes, true ambigrams are symmetrical at any angle, but they are nearly impossible to produce with amateur techniques, therefore black metal artists settle for the horizontal symmetry.
Satanic ambigrams were inspired in fact by the Illumnati, a secret society of intellectuals whose enemy was the church. The Illuminati may have been inspired by the Arabic examples you speak of.