Suppose for instance, you build a microscopic device that emulates the ability of a white blood cell, or bone marrow in order to heal a person's wounds. Well, you've still got to power it. If nanites were all run off of brownian motion and they're doing any degree of work, with any amount of speed, they'll be sucking up heat at incredible rates.
To be practical, medical nanites would need an external power supply and a means to direct that power through the body without cooking it.
The chair is actually running a series of different nanites through Jack's leg:
Some to help repair the bone
Some to help repair the tissue damage
Some to help keep the affected areas highly oxygenated
(After all, the body's own repair mechanisms have a few billion years of engineering
testing behind them, and have managed to do a pretty decent job without these pesky nanites getting in the way.)
Why a chair, instead of just a leg sized cast? They found that Jack's ribs still haven't completely healed from the earlier fractures when he was swatted by a lion.
Additionally: As some will have guessed, chairs are easier to draw.