No way that is possibly true. People realised they didn't have tests. A bunch of people of a liberterian bent or systems thinkers would have picked the FDA as the problem very quickly. But for most people diagnosing and rectifying that sort of snarl in a complex bureaucratic process would have taken about as long as it did. This happened at blinding speed for a bureaucracy fixing up its own problems.
There were compounding failures that required a government body to put their hand up and say "I have too much power" or "lets take a risk on letting some non-government actors take key roles". It wasn't going to work unless the executive happened by amazing luck of have an infectious disease specialist in a key role (maybe president or VP) who was already sweating at night about asymptomatic infections.
The problem is the legislative framework where first response in a crisis was to centralise the response on a single point of failure. It barely matters who the actors were, superhuman effort by one or two people can't reliably overcome a bad system. This should never have been a situation where the CDC making a mistake delayed the crisis response by months and nobody but the CDC/FDA had the power to fix that.