It's coming out of the insurance fund, which is paid into by banks. So the cost is still ultimately borne across a wider sphere, but not the government per se. (This is what's meant by "Any losses to the Deposit Insurance Fund to support uninsured depositors will be recovered by a special assessment on banks, as required by law.")

The costs aren't borne by "the taxpayer", but an awful lot of taxpayers who had nothing to do with this or even purposely avoided it may be paying higher banking fees as a result.