$$foo is not a shorthand for $foo->.

>perl -E"$foo=\'foo'; say $$foo;"
foo

>perl -E"$foo=\'foo'; say $foo->;"
syntax error at -e line 1, near "->;"
Execution of -e aborted due to compilation errors.
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You're probably thinking of the equivalency of $$foo[...] and $foo->[...] and of $$foo{...} and $foo->{...}, but that's already mentioned.