This is a nonsense. Having more or less fat has nothing whatsoever to do with healing. Roughly speaking and for the purposes of this discussion, your body is composed of four types of tissue arranged in layers. At the top the skin cells (to keep out infection and seal everything inside). Underneath those fat cells (for insulation and padding). Underneath that muscle cells (for articulation) and lastly bone cells (for structure and support). Each regenerate or repair differently, the presence of another type makes no difference to the others.
Now having some fat can act as padding against blunt force traumas (including anything striking armour). That's why rugby players, in addition to being very muscular, don't work to strip away all their body fat. However it's of no use whatsoever against anything sharp that lacerates or punctures the skin. Furthermore, fat alone isn't sufficient padding without the bulk of developed muscles underneath them. Just being fat, without being muscular isn't going to be of much use. Just being fat won't make you as strong as someone who actually works on developing their strength.
We're talking about human beings here, an elephant is completely irrelevant. Elephants have different skeletons, different musculatures and attachments, and precisely nothing that is applicable to this discussion of human strength. Not even apes count, given their attachments and musculature are different to humans.
Being able to jump is a simple measure of strength. I'm 65 kilos, I've run with a 100 kilo man on my back. Not far (shuttles back and forth across a hall with squats at either end) but it wasn't simply picking him up and putting him down again. I can leg press 150 kilos, so I'm confident I could move a 130 kilo man. Especially if I'm applying strength with some intelligence, rather than simply trying to go power on power. There is no linkage between fat and strength, that two things might sometimes occur together doesn't mean one causes the other.
There are fat people who are strong, but in modern societies there are a lot more fat people who are weak because they are sedentary.
There is no way someone who is training at the level a gladiator or professional soldier is wouldn't be muscular, regardless of how much fat they might have. The human body is now as it was two or more millenia ago, eat correctly and train it hard, and you develop muscles.
That painting was by Jean-Léon Gérôme, who created that in 1872. He had no idea what a gladiator actually looked like, he's just gone with what was a contemporary notion of how a strong man might look. Since he probably used a model who looked like that.
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