B::Deparse is maybe illuminating. In either case it looks like the LHS of the second assignment winds up being $z which is then assigned "false\n".

$ perl -MO=Deparse,-p,-q -E '($x) ? $z  = "true\n" : $z  = "false\n"; 
+print $z;'
use feature 'current_sub', 'bitwise', 'evalbytes', 'fc', 'isa', 'modul
+e_true', 'postderef_qq', 'say', 'signatures', 'state', 'unicode_strin
+gs', 'unicode_eval';
(($x ? ($z = "true\n") : $z) = "false\n");
print($z);
-e syntax OK
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