Phinney usually is more focused on a younger, more metabolically healthy, non-obese population. That’s one significant difference, versus Fung.
“Depleting essential protein stores” - the body really doesn’t store much protein, at all - not like it can do with fat or with carbohydrates (converted to fat). Sure, it can burn protein structures, if it has to, to gain energy to sustain life, but this is far down the timeline of what happens when we eat less or stop eating.
“Losing lean mass” can mean the effects of autophagy - using up harmful things in the body, faulty, damaged, old cellular components, etc. It can be getting rid of excess skin - and our skin is ~1/6 of our body weight, often. It can be less water in muscle tissue, as measured by a scan - while in reality it’s not muscle that’s actually been lost.
I’ve seen Phinney say some things about fasting that are demonstrably not true, and which effectively say, “There’s no such thing as autophagy.” That said, he’s due enormous credit for the truths which he has brought to light, and for which he’s lobbied long and hard - often in the face of daunting resistance.
The concept of “losing” stuff we need in our heart and brain is nonsense, at least in my opinion. At one time (and sadly I cannot find what I was reading, now) there was a Russian study on people who had starved all the way to death. The heart lost 3% mass, on average. Not that big a deal - from all I know - and dehydration and fat loss could more than account for it.
Witness the long fasts that many have done - lots of them around a month or more in length, up to the well-known one of Angus Barbieri, who went from 456 lbs/207 kg to 180 lbs/82 kg during a fast of 382 days. It’s not like his heart, brain, or other organs suffered, and he was essentially just fine (and maintained a healthy weight for years thereafter). While I do not know, I’d bet he lost a little muscle in there somewhere - assuming he could move, moving two and a half times one’s weight around likely would result in some muscular adaptation. Even if so, I’ve never seen anything to indicate he regretted losing the weight.