I can give a personal anecdote.
About 3 years ago I began experiments with paleo, I am 5'6-5'7 started over 190lbs and in about 4 months was down to 152lbs. Weekends I would have cheat meals usually a pizza day and burger/fry day.
Around then I began running for the first time in my life. I started out the first 3 months at 1 mile everyday, which I thought was a lot until a high school buddy laughed when I told him.
I stopped eating paleo and increased to 3 miles about 5 times a week. This went on for about a month, when I decided to register for a half marathon and started a basic 12 week training. I tried to restart paleo, but about a month in my legs began to hurt which I attributed to lack of carbs so I again got off. During Summer in Miami I decreased the mileage due to the heat and would get back on paleo still weekend cheat days.
During any of that time I didn't know about Ketosis or I never experienced anything I would call Ketosis.
Fast forward to this year, I completed the Disney Goofy (half day1, full day2), then another 2 halfs during the spring. I was back to about 170, and despite running more mileage than I ever had, I was not pleased with my physique, feeling I looked better even at the same weight while on paleo. So I decided after my last half of the season, I would try to go full paleo without any cheat meals on the weekend with the goal of 5 mile runs 4-5 times per week. I just completed a half the weekend before and Tuesday I did my 5 mile on paleo and felt fine/normal.
Wednesday/Thursday during my runs I got light head and basically though I might blackout, never experienced that before, but I stuck with it. Then by the 3rd week, I honestly felt I was tapping into a different energy source, not that I was running faster but it was just a different feeling and it was amazing.
Despite having combined paleo and running before, my body had never responded like this before. Having read up on high endurance athletes who do paleo after the fact, I believe what was happening is my body was tapping into and burning fat as its main source of energy and I also learned about Ketosis at that time (I believe/understand these to be one in the same, but they may not be). I will note, even my mind seemed different as I began to really think/feel that sugars were a poison and I was disgusted by the thought of breads/sugars, meaning I didn't even want cheat days on the weekend. This lasted for about 2 months without a cheat day and eventually there was a craving for carbs and I had no hesitation about giving in, so I am back off the paleo, and basically the very next run my body was not performing the same as it was. I look forward to implementing a strict paleo diet again without cheat days when the weather cools and I will try to build my mileage up in that state for the next running season.