The problem is that Trump himself doesn't understand what he is saying. He doesn't understand the difference between sovereign debt and real, private sector debt. He doesn't understand that a dollar is also a government liability, just like a bond is. He's an idiot.
QE was just an exchange of assets, bonds for reserves and account balances. Nobody's net financial position changed because of QE. The Fed expanded their balance sheet, holding a lot more bonds on their asset side, and on their liability side were a lot more reserves held by banks. Treasury still pays the interest on bonds, and the Fed (since QE) still pays interest on reserves. QE just meant that we paid a bit less interest (reserves earn less than bonds, usually); interest paid to the Fed (on the bonds they hold) is remitted back to the Treasury, after other Fed expenses (like interest on reserves).
I don't know what Krugman idea you were referring to, but if he was talking about zero-interest bonds (or, alternatively, the trillion-dollar platinum coin), those assets would sit on the asset side of the Fed's balance sheet, earning no interest. Which wouldn't matter, since the Fed remits its profits to the Treasury anyway.