Finally getting a chance to read through the post you linked. Some quotes/observations:
"Well so long that you’re throwing a few hundred calories of pure fat into your coffee, you will have less room to work with for your actual meals. What’s worse, butter/oil, on it’s own, does little to promote fullness."
Granted, this is just my N=1, and based on my experience with extended, not intermittent, fasting (though I sometimes do BPC on IF), but I definitely find that adding fat makes for less hunger on a fast.
"So those calories are going to make maintaining a calorie deficit harder than ever before. Not to mention the fact that butter and oils are extremely low in vitamins and minerals, rendering them a terrible source of nutrition."
Misunderstands both mechanism (seems to take the CICO attitude) and reasoning (not really looking to BPC for nutrients) behind the use of fat during a fast.
With respect to the section you originally quoted regarding the role of fat and suppression of growth hormone, and the follow-on difficulty in burning fat, I can only respond with my N=1 of having dropped around 4 pounds in 3 days on my current extended fast. Can't prove that's all fat, but I'm certain at least some of it is. Would I have lost more absent the fat in my coffee? Maybe. But I'm getting good enough results that if fat is what I need to make the extended fast tolerable, it seems like a reasonable trade-off.
I also take issue with the phrase "fat-only meal." Adding fat to coffee isn't a meal. It's not meant to be. And for those of us who are fortunate enough to no longer have sufficient body fat to fully sustain our energy needs during a fast, that extra fat may actually be essential to avoid messing with our metabolic rate.
It's certainly possible (perhaps even probably) that there are downsides to adding fat during a fast. But I am reluctant to accept a dogmatic statement that it should always be avoided. It is, however, good to understand the potential downsides when making the call on what works for you, so I appreciate you sharing the information.