Although I know this is how they work in the actual game of Blood Bowl as well as on Fumbbl, something about apothecaries struck me today as a bit odd. This realization struck me with the same force, and at approximately the same time, that one of my gutter runners (with mighty blow due to handicappage) struck stone dead a foolish high elf passer named Hunam.
The gutter runner was stunned (presumable because he had actually managed to kill somebody somehow) and the high elf, not wanting to die, called out in desparation for the Apothecary.

"Apothecary! Apothecary! I am calling out in desperation!" he cried.

The apothecary then rushed on to the field and applied his impressively masterful first aid. So masterful that the passer, who had been on the brink of death ("I can see the light at the end of the tunnel!" he exclaimed in a delirious bout of delusion, as his head, severed from his spinal column by a well-aimed punch, lolled forward on his chest) was now almost entirely unhurt! The poor gutter runner was so stunned that he continued to, well, be stunned.

In less silly terminology: Why should a player who was Badly Hurt, Seriously Injured, or Dead, after receiving apothecarical aid, simply be "down"? Considering what has just happened to said player, I think it would make much more sense for them to at least be stunned, if not KOed, representing their brave brush with death/injury/woundedness.