Yeah I don't get this objection. The president-elect becomes president when he's sworn in on the Capitol steps - a ceremony the outgoing president traditionally always is present for, but plays no actual official role in whatsoever. Trump and his entire cabinet could barricade the White House doors and obstinately refuse to leave and a solution to that problem would have to be worked out at some point but it wouldn't somehow make Trump "still the president", or mean that the federal departments still have to take orders from him and his cabinet.