Does "Access to own record" also covers transaction they submitted not on their own record?

We are trying to understand what 'Access to own record' do.

At the moment, this is disabled in the Person Security Profiles for our custom roles, and this is causing HR not able to view the Options like Terminate Process, Recover etc under the Action button in the Transaction Console for Failed Transactions.

Our question is When HR is conducting a transaction, they are not conducting it on their own record, they are just submitting transaction for employees. How come that they can't see these actions when they are not conducting transactions for their own record.

Does 'Access to own record' covers also the transaction they submitted not for their own record?