This looks odd to me. First you say you're running AIX 6.1, which is evidenced by the fact that xlC.aix61.rte is installed on your system (IIRC, it won't install on a 5.3 system).
And then your paths have "AIX5.3_64" in there. Which means that this can't be the system perl. (And AIX 5.3 seems to have come with perl 5.8.2.) The system perl would be:
$ /usr/opt/perl5/bin/perl5.8.8_64bit -le 'print for @INC'
(Actually, until about 5 minutes ago, I didn't even realise there was a 64-bit perl installed, so thanks.)
What this means is that I'm not sure I'm going to be able to replicate your issue very easily. On the other hand, my first suggestion is always to stop using the system perl anyway, and compile your own copy for your own use. It looks like you've already done that. I wonder if you recompiled the stack on AIX 6 if that would solve your problem. On the other hand, I'd suggest going to something a bit more recent ;-) - I have perl 5.16.1 passing all tests on AIX 7, I suspect this should work on AIX 6, too.
What does "file ../../AIX5.3_64/perl-5.8.8/lib/auto/File/Glob/Glob.so" say? For the system perl, I get:
$ file /usr/opt/perl5/lib64/5.8.8/aix-thread-multi-64all/auto/File/Glo
+so: 64-bit XCOFF executable or object module not stripped
so we'd want to compare here.