From what I was taught in my med school biostats class (and grad engineering imaging class) you'd want a screening test to have a high sensitivity. Remember the acronyms SpIN and SnOUT. You use a specific test to rule something in (high probability the person has the disease if positive result) and sensitive test to rule something out (high probability the person does not have the disease if negative result). A specific test has a low false positive rate and a specific test has a low false negative rate. Before you take someone to the OR you'd want a positive result in a highly specific test for their disease (let's say a positive tumor biopsy) so that you're not needless operating on people who don't have the disease.
With a screening test you're not as concerned about correctly identifying people who have the disease, so you'd want a sensitive test to rule people out. What you actually want is to be able to say to people who receive a negative result do not have the disease. People who receive a positive test result may or may not have the disease but can go for further testing with a more specific test (like a biopsy for breast cancer after a positive mammogram or biopsy for prostate cancer after high PSA) to determine who does have the disease. Again, with screening you're not necessarily identifying people with the disease you're looking for, you're trying to correctly identify people who you're confident do not have the disease so that you can avoid further testing and be confident that you haven't missed something. The false negative rate = 1 - sensitivity, so if you want a low false negative rate you want a highly sensitive test.
Are you sure MS didn't say you'd want high NPV? For a screening test, you'd want a high probability that a negative result means the person doesn't have the disease. A high NPV means that if you get a negative test result, the person is likely to be actually negative (low false negative rate), so a high NPV would be desirable for a screening test. The problem with NPV and PPV is that they're dependent on the pre-test probability of the disease whereas sensitivity and specificity are not dependent on pre-test probability.