First, charities are closer to research funders than grant recipients. They are more likely to hire contractors to do the actual work or just send the money instead of doing the work themselves.
Second, academic overhead rates are usually stated relative to direct costs. A 50% overhead rate means 1/3 of total costs.
Third, it's not just administrative overhead, but it's also used for paying for facilities and the services required for using and maintaining them. The actual administrative overhead, for administrative services and facilities used by the administration, is usually below 20% of the total.
Second, academic overhead rates are usually stated relative to direct costs. A 50% overhead rate means 1/3 of total costs.
Third, it's not just administrative overhead, but it's also used for paying for facilities and the services required for using and maintaining them. The actual administrative overhead, for administrative services and facilities used by the administration, is usually below 20% of the total.