My understanding is that reserves are injected when the Fed buys treasury bonds, engages in repo activity, makes a loan to banks at the penalty rate, or pays interest on existing reserves.

All true. It is often just easier to keep things simple as long as doing so doesn’t create a false assumption. Banks must balance their books every few days and the total of assets and obligations must be reconciled. The fewer interbank transfers that are made from an individual loan, the fewer reserve funds the lending bank has to borrow. It has many options from which to obtain the funds, but the general concept of money as an obligation remains true.