@Publisher While research universities have more research going on, the opportunities for undergraduates to do actual research are few and far between. The vast majority of undergraduates who work with faculty on research are doing manual work, from cleaning up to feeding animal research subject. Very few of these students ever do anything which results in even a conference poster, much less a peer-reviewed publication. Student research at LACs is much more likely to be actual research, which results in a name on a publication.
After studying, being a teaching assistant, teaching, and working at 6 research universities in 5 states, I have seen nothing to contradict this. Over 15 years of conferences and looking at student presentations have also done nothing to contradict this.
Proportionally, graduates of liberal arts colleges attain PhDs at a much higher rate than graduates of research universities. This is a fact. Since being accepted to PhD programs is extremely difficult without demonstrating background in research, this argues that LACs are better at providing undergraduates with more opportunities at gain this experience.
There is also an issue of LoRs - an undergraduate working in a lab at a research university is more likely to be working with a graduate student or a post-doc than with the PI, meaning that their Lor is likely going to be either from the grad student/post-doc
Of the 50 colleges with the highest percent of undergraduates who go on to get PhDs, 34 are liberal arts colleges and 16 are research universities (R1). Of the top 100, 68 are LACs, and 27 are research universities (both R1 and R2). You can derive this yourself from https://ncsesdata.nsf.gov/ids/sed but I let the good people at Swarthmore do the work for me: https://www.swarthmore.edu/institutional-research/doctorates-awarded.