It's "false reasoning" in the respect that the reasoning we're coming up with here is not the person's intended purpose. Sure, it can be a USB stick... sure, it can hold contacts... sure, it can be used for presentations...
..but if these weren't obvious uses to the person trying to get an iPod, that leaves us to wonder -- when that person asked us to justify an iPod in the workplace, why did they want an iPod in the first place? My guess: to listen to music and get a free iPod. There are other, cheaper devices that can perform all the tasks the iPod can perform better and cheaper, short of listening to music.
Still, the reasons listed here in this thread are good ones to justify an iPod in the workplace, but I think alternative solutions should be offered to the boss as well, and let him make the decision.
For example:
FireWire hard drive for backups: the only thing the iPod has going for it here is size, and that's no deal-breaker. There are faster, better, cheaper, more spacious alternatives.
Contact organizer/PDA: again, there are better, cheaper alternatives. Palm makes a great Zire, like the 21 and 31 that'll do much more than keep your contacts handy.
Emergency boot disk: ditto. You'd have to install OS X on it first, and that would cost $129 unless you've got a spare, legal copy that's unused. Then you'd have to add ~$100 for some troubleshooting software, like TechTool or DiskWarrior.
Voice recorder: ditto. Any Sony mini-cassette recorder will do fine.
Even adding all the alternatives up from each of these categories, I'll bet it'll still be in the $300 - $350 range ($100 external drive, $100 PDA, $30 voice recorder, $100 MicroMat TechTool Pro).
The only iPod I could recommend to a boss would be the shuffle. You'd be hard-pressed to find a USB flash drive with that kind of capacity and quality for less.