First of all, that post I made last night was after a long game of D&D and didn't make the point I wanted.
A 3-CON Wizard is going to heal up a greater percentage of max HP a night's rest than a 20-CON Barbarian. I think that's a head-scratcher, the same way that a Warlord's Inspiring Word can somehow make unconscious characters get back on their feet.
As I described before, I see little to no connection there at all. The "head-scratcher" only comes in if you force HP into real or abstract boxes.
The 3 CON wizard has vastly less HP than the 20 CON Barbarian. Now lets say an evil cleric has created two linked golems that both in perfect unison land identical blows, one on each. Let's add that the wizard is not killed by this blow. Now let's add that the encounter is resolved with zero further damage to either the wizard or the barbarian.
Now, what do we know? Very little.
We can assume that both characters took 4 HP or they took 25 HP, or whatever, it makes no difference.
The first important thing to note is that they will both heal from THAT WOUND in the same amount of time. (assuming they are the same level and they each heal naturally)
But how much of their total HP are physical and how much are fate? The answer is that there is no answer. No answer is needed. (Unless you are using surges in which case 100% fate is needed)
They took the same blow. But maybe the wizard took a lot more physical damage and the barbarian, who has a simply scratch from the attack that didn't manage to kill the wizard, probably dodged aside or deflected much of the blow. Certainly you wound not describe the effect of a 25 HP blow on a 20 HP wizard the same as you would describe a 25 HP blow on a 100 HP barbarian would you? I would not.
So when they are healing their respective 25 HP back, the wizard is, mostly, healing physical damage, while the barbarian is healing, almost entirely, his "fate" back.
There is no reason to be conflicted over comparing the rates of "fate" recovery and physical wound healing.