Your assertion, regarding the difference between $f; and &f();, doesn't ring quite true - consider

sub frobnicate {
  &foo;
  &bar();
}
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The statement &foo; calls foo using a mirror image of @_ i.e. as passed to frobnicate - whereas, as you point out, &bar() calls bar with an empty argument list - but neither call i.e. to foo() or bar(), modifies @_ as passed to frobnicate.