If the followup is testing the same thing with a different methodology, then the metaphor works.
Generally an idea is considered well supported when multiple methodologies support it, yes. In the psychology lab I used to work in, at least, we never try to replicate, but we do try to show the same thing in multiple different ways. There are maybe 15 different experiments a year, but they're generally all centered around proving or dis-proving a cluster of 2 or 3 broad, conceptually linked hypotheses.
Biology labs I've worked with do often do the whole "okay, the results are in and this is established now, let's find additional detail' thing, but that's because they were usually looking at much simpler systems, like a single protein or something, so they could afford to take liberties and not be so paranoid about experimental methods.
Jason Mitchell is [edit: has been] the John L. Loeb Associate Professor of the Social Sciences at Harvard. He has won the National Academy of Science's Troland Award as well as the Association for Psychological Science's Janet Taylor Spence Award for Transformative Early Career Contribution.
Here, he argues against the principle of replicability of experiments in science. Apparently, it's disrespectful, and presumptively wrong.
This is why we can't have social science. Not because the subject is not amenable to the scientific method -- it obviously is. People are conducting controlled experiments and other people are attempting to replicate the results. So far, so good. Rather, the problem is that at least one celebrated authority in the field hates that, and would prefer much, much more deference to authority.