GLOB and "global" are two different things. You can easily freeze global variables, but you can't freeze typeglobs, see "Typeglobs and Filehandles" in perldata.
bless our $x = , 'My::class';
print Storable::freeze($x); # No error, $x is global.
bless my $y = \*STDERR, 'My::class';
print Storable::freeze($y); # Can't store GLOB items, $y is le