This is not ENTIRELY correct. There are 2 reasons why you do testing.
1. To check how prevalent disease is
2. To check if a particular person actually has disease

What he says is true only for (2)

Assuming the error rate of testing is random, you MUST test more for (1). https://twitter.com/karthiks/status/1250362089585033216
Which is precisely why u pick up a person who tested +ve and re-test him/her. Because u want to reduce probability of false positives. The first case is more abt Central limit theorem and the second case is more about Bayes theorem.

Countries are not stupid to do more testing
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