The fact that the financial institution knows that any part of the distribution is nontaxable means that the distribution is not from an IRA. A financial institution has no way to know if any particular amounts distributed from an IRA are taxable or not.
As VolvoGirl said, the both pre-tax and after-tax portions distributed count toward the RMD for that account.
The point of retirement accounts is to supplement income during retirement, so Congress put provisions into the law to make sure that these funds would eventually be distributed, preferably to the employee rather than to the employee's beneficiaries. As you pointed out, it also makes sure that the collection of taxes on this deferred income would not be pushed out to the future indefinitely.
If you are inclined to make QCDs, the funds in a qualified retirement plan could be rolled over to an IRA after having completed the RMD for the year. In this case, since the funds have an after-tax component, the rollover could be split between traditional and Roth IRAs with the pre-tax portion going to the traditional IRA and the after-tax portion going to the Roth IRA. After that, you could make QCDs from the traditional IRA.
