[andreilys]

Ignoring all the true and false negatives which themselves are markers of how accurate the test is.

16% precision is the correct statement, saying the test is wrong 84% of the time implies that those getting negative results might actually have positive results.

[robbedpeter]

He framed his statement correctly, limiting his observation to the condition that the test returned a positive result. Saying that 84% of positive results are false is correct if only 16% are true. You'd need to know false negative rates and base occurrence rates (modified by whatever other factors are unique to your situation) to inform the nature of information you get by performing the test.