Let's suppose you inherited some stocks or mutual fund investments held at a stock broker. Those assets would all have received a stepped up value when the previous owner died, so you pay income tax on current interest and dividends, plus you would pay capital gains if you sell the investments based on the selling price compared to their value on the date of the previous owner's death.
If you add money to that investment account (it doesn't matter from where) then you are buying new shares at the price on the day you buy them. You will pay tax on current interest and dividends, and you will pay capital gains tax if you sell the shares for more than you paid. But you don't pay tax again on the original investment. That's not a benefit of the account being inherited, that's how any investment is taxed. If you had taken the RMD and put it in a regular savings account, you would pay tax on the interest. If you had bought collectible comic books, you would pay tax on the increase in price (the gain) when you sell them. If you put it in your mattress, you wouldn't pay any more tax, but you wouldnt have any more income from that money and it would gradually lose purchasing power due to inflation.
