Effects of changes in fat, fish, and fibre intakes on... [Lancet. 1989] - PubMed - NCBI
Low-fat dietary pattern and risk of invasive breast can... [JAMA. 2006] - PubMed - NCBI2033 men who had recovered from MI were allocated to receive or not to receive advice on each of three dietary factors: a reduction in fat intake and an increase in the ratio of polyunsaturated to saturated fat, an increase in fatty fish intake, and an increase in cereal fibre intake...Subjects given fibre advice had a slightly higher mortality than other subjects (not significant).
Also notice the lack of difference in mortality rates.The intervention was designed to promote dietary change with the goals of reducing intake of total fat to 20% of energy and increasing consumption of vegetables and fruit to at least 5 servings daily and grains to at least 6 servings daily....Among postmenopausal women, a low-fat dietary pattern did not result in a statistically significant reduction in invasive breast cancer risk over an 8.1-year average follow-up period.
The Paleo diet explicitly forbids grains. Here are some studies on the diet:
A Palaeolithic diet improves glucose tolerance ... [Diabetologia. 2007] - PubMed - NCBI
Long-term effects of a Palaeolithic-type die... [Eur J Clin Nutr. 2014] - PubMed - NCBI