Unless I'm misreading what you're saying, I think you have Bayes's rule confused in that statement. If 75% of positive results are false, that's actually right in line with what you might want for a first screening.
Of course, you want to know not just P(X|Y), but also P(Y|X) -- you really need the joint distribution to determine how useful the test is.
For a rapid screening, you generally want a low false negative, and you're willing to compromise by having a high false positive rate as a result. The real thing you care about is P(test positive | have MDD), not P(have MDD | test positive). You don't care about the latter (within reason - obviously you could just have everyone test positive, but you're also trying to maximize the former probability subject to some constraint - usually time/money).
Psychiatric conditions are notoriously difficult to test/evaluate/treat because they are oftentimes heterogeneous, so I don't know what kind of numbers we should be looking for in this case, but I just wanted to clarify that having a majority of people who test positive ending up being healthy actually doesn't necessarily rule a test out as being a useful rapid-response screening, in the general case.