Everyone gets caught up on the 72 hour phrase. It is actually three days before departure from the USA. We ran into that two weeks ago. The CDC website clearly states three days. The example they give is if your flight leaves on Friday, regardless of time on Friday, then the test can be done at any time of Tuesday.
We leave for Botswana on this Friday, our PCR tests are scheduled for Tuesday. Most places take the test throughout the day, then send them all to the lab at 5PM that afternoon, with the lab getting started on testing your sample the next morning. Then add 24-48 hours for your result to come in an email.
When we landed in Johannesburg, on Qatar, the fella at immigration saw the time on the card was beyond 72 hours and he called his boss over. She looked at the papers, then gave him a look like "you're an idiot" and said something in Afrikaans to him. He apologized to us and waved us through.
And we were sent a form that looks like an official form from Qatar Air. We had them ready at the check in at Houston. They asked what that was and we told them we were told to have it filled out and ready to give to you. They said they had no idea what it is and we tossed them in the trash.
All they needed was our passport and the PCR test. From the point on, they wanted to see your passport, your PCR test, and your boarding pass. On the way back, leaving Cape Town on Qatar, they looked at our new PCR tests results at check in, then they were never asked for again. Not to board in Cape Town, not on our layover in Doha, nor in Houston when we landed. Just passports and boarding passes.
Flying Ethiopian this next trip, that will be a first, and I'm sure it will probably have a different result.