Another possible explanation for the statistics is that almost no liberal arts colleges have either engineering schools nor offer business degrees. People in these fields rarely pursue a Ph.D. Students interested in engineering are simply not likely to choose a liberal arts college. At many research universities, and perhaps most state universities, the most popular major is business.
In other words, it might have less to do with LAC’s preparing students for grad school, and more to do with research universities offering bachelors degrees which lead directly to a job. If we removed engineering and business majors from the statistics, the gap in Ph.D production would definitely be reduced, and might come close to equalizing.