Anaphors in many languages do not obey the 'canonical' Binding Condition A (Chomsky 1986), such as Icelandic 'sig' and Mandarin 'ziji'. Two main competing approaches have been proposed to capture binding beyond the local domain: (i) The LONG-DISTANCE BINDING (LDB) theory derives non-local binding via covert cyclic movement and turns non-local binding into local binding which always obeys Condition A. (Pica 1987, Huang & Tang 1991) (ii) The LOGOPHORICITY (LOG) theory explains exempt anaphors by logophoric rather than pure structural constraints (Sells 1987, Huang & Liu 2001, Charnavel 2019). The two theories make distinct predictions on the referential dependencies between reflexives and their antecedents. The LDB theory predicts that antecedents should always c-command the reflexives, while the LOG theory predicts that reflexives need not be c-commanded by their antecedents if they are logophoric. This paper aims to experimentally test the two competing theories by investigating the binding conditions of Chinese reflexive 'ziji' and 'taziji' using acceptability judgment tasks. The results about 'ziji' support the LOG theory against the LDB theory. Furthermore, our results reveal that 'taziji', though usually considered as a local anaphor (e.g., Cole, Hermon & Huang 2006), can in fact similarly be exempt from binding under logophoric conditions.