I think your hypothesis is implausible that industry-sponsored research is more incorrect or less reproducible than non-industry-sponsored. Or can you give some reasons for this assumption?
On the contrary looking at many of the meta-surveys (partly conducted by industry, because non-industry-sponsored research maybe is less reproducible to their experience) that investigated the reproducibility of academic research in the recent years, rather the opposite is maybe the case and known within industry.
Additionally, I don't see how it makes a difference if money financing a PhD student comes from industry or not? Wouldn't the rationale rather be, if money is spent by industry, then rather PhD scientists/Professors are hired for a project than cheap and still learning PhD students pressured by publish or perish? And to my knowledge more of the spotted scientific misconduct has been caused by untenured researchers. Again, publish or perish
And when industry research can't reproduce 70–90% of academic laboratory findings, then a better question is probably if most of the research projects are funded by industry or not and what kind of researchers are on average hired for industry-sponsored projects (PhD students, PhD's, tenured)
What maybe sounds plausible, that researchers carrying out industry-sponsored projects tend even more to make up results or buzzy headlines ("new battery technology allows charging up within 10% of normal time" which I read every month or so), is rather implausible to me, because important and valuable results in industry-sponsored research projects are often rather published as a patent than a paper.
More importantly, there is a clear correlation that research in branches being strongly entangled with industry (engineering, physics,...) is much better reproducible than weakly linked branches (social sciences, psychology, biomedical,...). Most of the meta-surveys are in such fields.
To take up your case of drug development, such only become legalized after 10 years of clinical trial, so I think the incentive for some PhD student is not significantly higher and often the PhD students have no clue if the money financing them comes from industry or public. And professors being biased by the funding source mostly don't conduct and evaluate the experiments and would have to alter the results (which also happened, but rarely)
Summa summarum I think there is no such study (my googling didn't find one but many meta-survey on reproducibility partly published by industry companies), as your hypothesis looks very implausible to me. There is probably a good virtual database with so much meta-surveys and the necesssity to name funding sources in a paper, still to me the important question would be, which kind of researcher (students, tenured,...) are typically hired for non-/industry sponsored projects? Because, the conclusion from the published meta-surveys in social sciences, psychology, biomedicine and the low reproducibility to be drawn is not that researchers in such fields tend to be more biased, tricking, cheating and therefore more incorrect results are published, but rather that industry is not much interested in such results and the level of scientific rigor is much lower than in hard sciences like quantitative physics or engineering, for which I didn't find a single meta-survey.