But this is a problem that can be tackled, and those who take it seriouslt already do so. For example, in our pipelines we use an infrastructure that always adds every command executed on the file, with every exact parameter, to the metadata of the file, starting from one canonical archived file - and hence, one can indeed reproduce manually the result of the pipeline given sufficient time and dedication. [Edit: we also write the git shar1]
The same way that say, biology labs have processes they engage in in order to convince us that their samples are not contaminated, we can have processes that lead to the reproducibility of data.
i'm not sure what problem you're talking about - someone reproduced the results with separate code and data, so what's to worry about? (i don't mean that because it was confirmed it was ok, but rather that if it had been wrong, we would have known in the end... after all, people make mistakes all the time - science is a collective enterprise that relies on many overlapping, interlocking pieces)
[Yeah, didn't I share an office with you 15 years ago? :-) ]
But data can't always be reproduced - Shoemaker-Levy won't hit Jupiter again any time soon, and while big results will cause a rush for verification, the little steps are usually believed as is. Moreover astronomy is a special case where - let's face it - if we go down the wrong path for a decade or so, nobody's bleeding.
Take on the other hand the processing of climate data - if crap engineering (not malice) causes garbage to come out of the data, this is a problem for everybody. So I think the OP is right in that proper auditing of computer-processed science data should be possible, I was just pointing out that it's not as hard (technically) as people think to achieve.
The same way that say, biology labs have processes they engage in in order to convince us that their samples are not contaminated, we can have processes that lead to the reproducibility of data.