It's my understanding that with just a linux image on a memory stick or mp3 player is usually connected via USB. Lots of BIOS are capable of booting USB devices, some are not. Similar to some BIOS don't allow booting from CD or DVD, while others will but have been set to boot from hard drive first. If the BIOS doesn't "know" to look for bootable USB devices, then it's not gonna look for them is it. Likewise if the BIOS isn't capable of booting from a USB device then again it ain't gonna boot from a USB device etc etc.
It's not something I've ever bothered to look into as when I first played with Linux (about 5 or so years ago) USB still had quite a lot of "teething problems" (TBA it could be a complete PITA). So I try to avoid it (habit) and run my printers and other peripherals via ethernet.
Plus, at initial boot stage (if I understood correctly when I was last reading about this) "it" won't, unless it knows to, look for USB devices.
Confirmation of how this is actually done is just a google away. It'd be better to check there as I couldn't say how easy/difficult this might be.
edit: just had a quick google myself and this
was the first hit. Sure it's refering to knoppix, but if knoppix can be booted from a memory stick then I'd guess it's "doable" for other distros