"Is that not the case?"

It's amazing the resources available from the IRS:

https://www.irs.gov/pub/irs-pdf/i1120w.pdf

"However, if the corporation does not want to use EFTPS, it can arrange for its tax professional, financial institution, payroll service, or other trusted third party to make electronic deposits on its behalf. Also, it may arrange for its financial institution to initiate a same-day tax wire payment (discussed below) on its behalf. EFTPS is a free service provided by the Department of the Treasury. Services provided by a tax professional, financial institution, payroll service, or other third party may have a fee."