From Jonathan Bernstein:
The real answer here is that it almost certainly doesn’t matter whether the president actually gave a formal order to slow down testing. That’s because we know that Trump just doesn’t have very much clout in the Trump administration. His orders are often ignored. To be fair: Many presidents have great difficult controlling executive-branch departments and agencies. But Trump seems to have an unusual amount of trouble within his own White House. That’s clear in the Washington Post’s recent reporting about the administration’s infighting over the next round of economic relief, in which Trump is presented as at best one minor voice among many in the discussion. Trump, we’re told, has decided to support another round of direct payments, but no one in the White House seems to care — not even enough to keep their lack of respect for his decision quiet. So my best guess is that if Trump ordered people to slow down testing they would’ve ignored him.
That said, Trump’s overall coolness on the subject probably did have some effect. Bureaucracies tend toward the status quo. Presidential leadership matters in encouraging action, especially quick action. That kind of leadership certainly hasn’t been apparent during the pandemic. Trump’s public statements have waffled between outright hostility to testing and a kind of “Mission Accomplished” swagger about having ramped it up.