That seems more than fair. You’ll certainly have better reliability if the recording device’s odds of failure are uncorrelated with the (notoriously excellent) game-related software out there.
To the best of my knowledge, your independent device will still have to be a PC in its own right. On the plus side, the CPU requirements of supporting a capture device(USB or PCIe) are comparatively modest, so you might be able to get away with one of those nice little cheap and compact AMD APU boards, maybe even one of the less crippled Atoms, though those tend to be pretty weak on storage, which isn’t good for a video recording box.
Especially if use at multiple sites is a consideration, you could put together a nice little build based on a variant of the ‘performance miniATX’ stuff that has become popular with the LAN party crowd. That’s a small, portable, case; but with enough PSU for a few HDDs, enough airflow for everything, probably even enough space to mount the capture device internally and bring just the capture and passthrough connectors to the exterior of the case.
(Not strictly related; but also of note if you want portable: the old Motorola Lapdock provides a 1366x768 display, HDMI-fed, touchpad, keyboard, and enough battery to power the lot for multiple hours in a reasonably attractive laptop-like package. Conveniently, the product was largely a failure, and now infests ebay at and sometimes below $50. Guides for using them to control devices that aren’t the one Motorola cellphone they were supposed to work with abound. Dragging around the mouse, keyboard, and monitor has traditionally been a real sore point for portable/secondary PC builds, so you might want to check one of those out if you end up building a freestanding capture box. They aren’t very pleasant as a primary set of peripherals, or at least I’m spoiled; but I have a few that come in very, very, handy for rPi, beaglebone, and assorted similar ‘just need some sort of console without sacrificing large amounts of desk space or shelling out for a non-VGA KVM switch’ applications.)