My first guess was that it was meant to be "ass-covering". A "sphincter" is a generic type of "circular muscle that normally maintains constriction of a natural body passage or orifice", of which there are "over 60 types in the human body" (Wiki), but there's only one sphincter people usually talk about (outside scientific literature). Looking more closely at the definition of the "per-" prefix, I get "through"[1], in which case a "persphinctery" statement is most directly defined as one that "came out of someone's ass".

[1] http://membean.com/wrotds/per-through