I'll stick to my assertion that asub can properly be deemed a "method" of main for | for the purposes of  -> invocation (although I have to agree that this terminology (update: and usage!) is a little bit perverse): it follows all the rules for class and object reference invocation. And  main::$x() can even be made to work (sorta) without strictures (which were invented (update: in part) to put a stop to this kind of madness) if the string variable is a package variable and syntax is as documented.

c:\@Work\Perl\monks>perl -wMstrict -MData::Dump -le
"sub func { print qq{hey @_}; }
 my  $symref = 'func';
 our $symref = 'func';
 ;;
 my $mainobj = bless [];
 dd $mainobj;
 ;;
 main->$symref('ho');
 $mainobj->$symref('there');
 ;;
 &$main::symref('nonny-nonny');
"
bless([], "main")

hey main ho
hey main=ARRAY(0x157618c) there
Can't use string ("func") as a subroutine ref while "strict refs" in u
+se at -e line 1.

c:\@Work\Perl\monks>perl -w -MData::Dump -le
"sub func { print qq{hey @_}; }
 my  $symref = 'func';
 our $symref = 'func';
 ;;
 my $mainobj = bless [];
 dd $mainobj;
 ;;
 main->$symref('ho');
 $mainobj->$symref('there');
 ;;
 &$main::symref('nonny-nonny');
"
bless([], "main")

hey main ho
hey main=ARRAY(0x185614c) there
hey nonny-nonny
[download]

c:\@Work\Perl\monks>perl -wMstrict -MData::Dump -le
"sub func { print qq{hey @_}; }
 sub bonk { print qq{zot @_}; }
 ;;
 my $symref = 'func';
 ;;
 use vars qw($symref);
 $main::symref = 'bonk';
 ;;
 my $mainobj = bless [];
 dd $mainobj;
 ;;
 main        -> $symref('ho');
 'main'      -> $symref('hi');
 my $mainstring = 'main';
 $mainstring -> $symref('he');
 $mainobj    -> $symref('there');
 ;;
 no strict 'refs';
 &$main::symref('nonny-nonny');
"
bless([], "main")

hey main ho
hey main hi
hey main he
hey main=ARRAY(0x37716c) there
zot nonny-nonny
[download]

Update 1: Changed example code to better illustrate difference between lexical and package variables.

Update 2: And BTW, this even works (under strictures!) with aliasing:

my $str = 'aaa';
for my $alias (main::, 'main', $mainstring, $mainobj) {
  $alias->$symref($str++);
  }
[download]