The point made in [29124] gets confirmed by the reactions to (7) and to (8) by the native speakers of English and Japanese, respectively.

(7) *John feared that the FBI (rather than the CIA) might assassinate himself.
(8) John-wa (CIA zya nakute) FBI-ga zibunzisin-o ansasutu suruno zya naika to osorete ita.

(8) is a fairly accurate translation of (7). (i) is not acceptable (unless in a dream or something) (presumably because the act of assassination can be done only to others not to oneself) and furthermore the FBI, being 'non-human', cannot be an antecedent of himself, anyway.

(i) #/*John assassinated himself.

The embedded subject therefore cannot be an antecedent for himself in (7). The matrix (i.e., main clause) subject John, one might think, may be a possible antecedent of himself, i.e., one might think that it may be possible for (7) to mean (ii).

(ii) John feared that the FBI (rather than the CIA) might assassinate John.

But the native speakers' judgments on (7) seem quite clear on (7); they reject (7). And such a judgment has been attributed to a principle that is part of the Computational System and to some formal property of himself.

If zibunzisin in Japanese had the same formal property as himself in English, (8) should be rejected as clearly as (7) is.

The Japanese counterpart of (i), given in (iii), is as odd as (i).

(iii) #/*John-wa zibunzisin-o ansatusita.

Yet, (8) is readily accepted by native speakers of Japanese.

The native speakers of English can check their own judgments on (7) and ask native speakers of Japanese about (8), and the native speakers of Japanese can do the 'reverse', to check the validity of what is reported above.

One might try to make a stipulation that accommodates the acceptability of (7).

But I see no plausible way to do so without making the claim (i) not refutable.

(i) Zibunzisin in Japanese has the same formal property as English himself