To be caught bang to rights means to be caught with irrefutable proof of wrongdoing, which is what happened with the baby eater.
Consider the statement "The baby eater of Bromsgrove had recently been sent down for life, caught red-handed with overwhelming evidence and no possible defense.". Is the statement "The baby eater of Bromsgrove had recently been sent down for life, caught bang to rights." false? Yes/no/unknown