There are various ways of looking at it. What I meant was that the fighter is pretty much the same as the dragon physically. What if the dragon's capacity to withstand damage had been condensed down into a 6ft tall, 235lb body? The explanation for this is magic. Just like the dragon, the fighter's hit points are 100% physical.
It could be argued that this is pretty similar to Gygax's idea of hit points representing many different non-physical qualities such as luck, skill, sixth sense, and magic. My idea is that instead of hit points being, say, 40% physical and 60% magic (or other non-physical property), they are 100% physical, with the explanation being magic. (By strict 3e terminology it would be called an extraordinary ability, rather than magic, like the barbarian's damage reduction, so the fighter keeps his hit points in an anti-magic field.)
There's always the issue in D&D that hit point loss doesn't incur any penalties until the total is reduced to zero. This is equally an issue whether one regards hp as physical or non-physical, and equally an issue for the big, tough dragon or little tough fighter. I would see all hit point loss prior to zero as real wounds - cuts, bruises, etc - that probably look nasty but are "just a flesh wound", though not in the Black Knight sense. As with pemerton's interpretation, the high level fighter on 50/100 hp is just as wounded as the low level fighter on 10/20 hp. They are both halfway to being incapacitated. The high level fighter probably sustained a greater number of separate blows but the cuts are less deep because he, like the dragon, is tougher.
This still leaves the problem of healing. The high level fighter on half hit points ought to recover just as fast as the low level fighter, if they are both equaly wounded. In 1e the recovery rate is 7 hp per week, plus Con bonus (until four weeks pass, at which point one fully heals). In 3e the rate is 1 hp per level per day - more proportionate to total hit points, but still not completely proportionate. For the proposed interpretation to make sense, hit points would have to be restored as a percentage of the total, which is how it works in 4e. This is all equally true for healing magic, which works at a flat rate pre-4e.
The biggest problem for the above interpretation is the warlord, as an important part of the class is that its abilities are martial, not magical. Hit points became less physical in 4e and this approach goes in the opposite direction.