In my mind (it's scarey in here), having more headroom doesn't necessarily mean that your system can take a *louder* signal. In a digital system 0db is always the "loudest" anything can be. Hear me out.
In *theory* you can record 48db lower in a 24bit system and still have the same bit resolution (e.g. 8bits*6db = 48db) as a 16bit system. But of course in the real world you don't get a full 144db of dynamic range out of a 24bit converter. While you'd be maintaining bit resolution (e.g. the number of values used to represent an audio signal), you'd run into a lot of mechanical/electrical/*real life* noise. I think think that the noise floor specs I've most often seen for 24bit systems have been in the -100 to -110db range.
At any rate, if you push the meters in a 16bit system you are using 65,536 discrete voltage levels to represent your audio stream, and your noise floor might be at -90db. But if you're on a 24bit system with 110db of dynamic range, which is 20db lower than the noise floor of the 16bit system, and you record such that your levels are down at around -20db, you are still sampling with a resolution of over 2 *million* discrete voltage levels, and with the same amount of real dynamic range as the 16bit sytem.
When you turn up the 24bit file from the above example by 20db (assuming the gain increase is constant), you end up with what is essentially the equivalent of the 16bit file that was tracked in the yellow. Therefore, in this example, you can record in the -20db range on the 24bit system without sacrificing fidelity, and have a whole lot of extra room for that guitar player who suddenly decides to go crazy.
Of course those are just a bunch of stupid numbers. In real life I don't know squat...but technically, it does demonstrate that you can track lower which essentially means that you have more headroom. Of course we could get into an argument over the meaning of headroom or something...but to me it's all relative.
Slackmaster 2000