But what does "measuring more directly anyway" mean if you're trying to measure something that may or may not exist?

For instance, in searches for new phenomena in high-energy physics, one usually puts an upper limit on deviations from the expectation of "known physics" (i.e., standard model). That essentially translates to statements like "if this particle exists, its mass should be higher than X TeV, or else we would have seen it already in our data". Of course, in reality, the particle probably does not exist, so you cannot really measure its mass!