What they are saying is that in populations with low infection rates a large percentage of positive tests will be false positives.
Of course that is true. If a population has a true infection rate of 0%, then the false positives will constitute 100% of the reported positives.
If a population has a 1% true infection rate and the test has a 1% false positive, then the testing will report about 2% positives and the false positives will constitute about 1/2 of the reported positives.
yep