The accuracy of the test in clinical practice does not mean that the test itself is useless, it means that there are other factors such as the way swabs are taken, the number of samples, the timing of the swabs and where the swabs come from, nasal swabs, urine BAL etc… Also as stated a positive result is more significant than a negative result. This is not really a reflection on the test itself. In a fast moving situation, practice evolves and what this paper is saying is that the practice of swabbing and the interpretation of results is important.
So if you are well today and have a swab which is negative then you become ill two days later and the swab then is positive, it does not mean that any of these tests were unreliable, it just means that there was not enough virus two days ago to be picked up on testing on the first occasion.
I am not sure what the reference for the bit on the block quotes is, could you please provide one?