It's all about training your body to burn the right fuel at the right time... Paleo, CKD, etc etc can help get you there, but there is no need to strictly adhere to them. Mike T. Nelson's Metabolic Flexibility is where it's at. I cut 2.5% bf and gained over 5 lbs of muscle in a month using one of the programs from Geoff Neupert's "More Kettlebell Muscle" (kb complexes, this particular program was 9 weeks) combined with stuff I learned from Mike T. Nelson ... Variability in diet was a big factor, for a month I ate 5-6 meals a day, next month only dinner (Warrior diet), this month is Leangains. Definitely didn't avoid junk food, definitely cut calories during the week(between 1200-3200 weekly deficit, RMR values determined by gas exchange test), cycled carbs(only had starches after my most intense training sessions), and actually reduced fat intake to under 80 grams 5-6 days a week. Eating "clean" all the time is overrated. Solid programming, keeping a food journal to keep you honest, and actively reducing emotional stress finally got me under 15% bf.. The only cardio I did was one or 2 Spin classes a week.FWIW, YMMV.... I have before and after pictures if anyone is interested. The only muscle building supplements I used were creatine, beta alanine, and milk protein concentrate. I also use GABA, melatonin, 5-HTP, powdered cal-mag, and sometimes ashwagandha to help improve quality of sleep.
"Paleo" is kinda silly, and not practical in the world we live in. Plus Big Macs are kinda really delicious. So are Frosted Mini Wheats and pancakes. In the end you have to figure out what works for you because nothing is one size fits all, just don't cave to fads...