Also, I agree with what you're saying in principle, but it seems that if they can handle the access from multiple users over one interface, they should be able to negotiate the access of multiple users over multiple interfaces.
You'd think that, but no. There's two things in that NAS HD - a NAS, and an HD. And they have different characteristics and spheres of responsibility here.
Very broadly, and without being super-technical:
First off, most interfaces (like SATA, which is what the USB is probably converted to) are hard-wired around the assumption that the computer on one end has complete and exclusive access to - "owns" - the disk on the other end.
As a result, computers accessing SATA hard drives often make certain assumptions, cache directory information in RAM, etc., which can cause crazy misbehavior if some other computer somehow manages to write to that disk in the interim. (Like, the two computers overwrite each others' data.) Watching it happen is a bit like imagining a "shadow me" going through yesterday morning's routine 15 minutes ahead of me this morning. My toothbrush isn't where I left it, the coffee's half gone, and my shoes are missing so I wear the other ones. But it's when I open the garage and the car is missing that the SHTF.
When you plug the NAS/HD into a USB port on the computer, that's a signal to the NAS controller to sit down, get out of the way, and yield direct ownership of the HDD over to the USB port, nd whatever's on the other side.
The NAS functionality - file sharing - is completely different, because a single computer (the NAS controller) actually "owns" the disk(s) and arbitrates access to individual files - not access to the disk itself - over the network.
Enabling NAS with the onboard controller and USB access at the same time would require two computers to "own" the disk at the same time, which is a no-go. Ideally, you'd plug it in via USB to your TV, and your TV would also be capable of doing the NAS stuff. (It probably is, at its core, if it's just running some Linux derivative. But hacking that would be a trick.)
For instance, I can attach an external device to my PC and share it. This is essentially the same thing and I'm surprised no open source components being leveraged support that kind of interaction.
Well, it is and it isn't the same thing, as outlined above. The closest thing you could do with FOSS software would be to create an iSCSI LUN and attach it to more than one system. In which case you'd get the overwriting-each-others'-data behavior I mentioned earlier.
The things I can think of that would resolve your issue:
1) "Fix" your WiFi. (Faster connection, better antennae, something to make it usable for streaming video.)
2) Direct-connect NAS HDD to the TV via wired network, access files over WiFi from elsewhere. (This would involve restructuring your network somewhat, and possibly adding a WiFi bridge or repeater, and a switch.)
3) Build a combination file server and media center PC that would drive the TV, play your videos, and share files out over your network.