I'll not delve into the whole "debate" between people who think significant amounts of weight loss can occur from other things than diet modification and exercise. Instead there's some simple proof on his own website that the picture isn't coming from his low-sleep "Paleo+" diet alone.
Quote from his article discussing his 4500 Calorie diet comments section:
Donna Clements: are you kiddingme? Those are your abs WITHOUT exercise? How in the world can that be so
Dave Asprey: I am entirely serious. It’s because I stack mTOR by using coffee with Bulletproof Intermittent fasting. mTOR builds muscle.
So it's confirmed that the diet outlined in your question didn't result in his abs by itself.
And no, I wouldn't trust him about that either. He drinks his BulletProof coffee to "stack" mTOR even though Caffeine is an mTOR inhibitor.
There are a bunch of other red flags in the link provided in your question, but aside from the usual extremely biased or non-peer-reviewed websites he links to and unpublished studies, I found this one particularly hypocritical:
A diet high in saturated fat improves blood vessel function (don’t be fooled by the title of this study, read Chris Masterjohn’s take on what this study actually showed). (35, 36)
What was the name of the study?
Consumption of saturated fat impairs the anti-inflammatory properties of high-density lipoproteins and endothelial function.
Just a quick term definition: "Endothelium" is your vascular tissue. Your blood vessels. The study concluded that:
Consumption of a saturated fat reduces the anti-inflammatory potential of HDL and impairs arterial endothelial function.
So what does Chris Masterjohn (who is apparently a PhD student at the University of Connecticut) say?
This is, of course, a hypothesis. I have not shown conclusively that the effects observed in the study must have been due to vitamin E [instead of saturated fats]...
So Dave Asprey is taking a hypothetical refutation of a study over the study itself as evidence that it's perfectly fine to high levels of saturated fats while still claiming the diet itself is based on science.