1) In the computer's registry, there's a public IP that was assigned to the user's account.
2) The IP used to share music was assigned to the user's account.
1) At some point, perhaps most recently, the computer was connected directly to the modem. Many users (especially my family) do this out of frustration with their router. Moreover, as other commenters have suggested, there could have still been a router while the computer maintained the public IP.
2) It's probable that the music was shared from someone connected somehow to the defendant's modem, but even that's not definite. IP's can be spoofed, or the RIAA may be wrong - check their methodology. i.e. if they check the IP by sending a message to the Kazaa user saying "l0l y0 dud3, wh4t's y0u4 1p?", the IP's not necessarily reliable.
Moreover, I didn't see anything discussing MAC addresses in there. Though they're eminently spoofable, they at least give you some idea of what network interface card you're talking to. If the RIAA does whip out the computer's MAC as evidence, you can simply point out how nearly every consumer wireless router offers MAC cloning.
In short, I think the best option would be to show in court how a normal customer might configure a computer connected to a router to have the public IP and have the router clone the computer's MAC. This would take a PC, a cheapo wireless router, and about 1-2 minutes. Then ask the expert how he'd know it was that computer, and not someone parked outside in a van that did filesharing. If he can't prove the PC had the public IP at the time the RIAA claims it was filesharing, even better - only MAC spoofing (or not even that if a MAC isn't produced as evidence) would need to be turned on, and that's a simple checkbox in router configuration. It might be worth researching if, at the time, that was required to get Verizon working with a router - ISP's have been known to tie accounts to MAC's. Even if not, some installation guides recommend simply checking the box to avoid the issue altogether. I simply fail to see how his testimony is incompatible whatsoever with there being a wireless router on the defendant's network either at the time of file sharing or at present. His vigorous handwaving about checking the registry suggests to me that, no, there's nothing there.
The one wrench in things would be if there's no evidence the computer was ever assigned a private IP. At this point you'd have to fall back on the possiblility of having a router while maintaining the public IP, which is more tenuous. You could also question how long the IP cache has been maintained, or use the following (I think better) argument: the "expert" wants to have his cake and eat it too, and winds up contradicting himself. On the one hand he says there's no value to this drive - it just *can't* be the one he's looking for. But then he turns around and bases his wild no-wireless-router claim on a registry entry! So which is it...is the drive in or out?