God, while trying to crack this, I even went so far as to consider hacking my MemoryStick reader-endowed Sony MSAC mouse’s driver, and in the end, the solution was as simple as unticking one item (Tools > Options... > Advanced > General > Use autoscrolling) in Firefox’s settings.

I think the naming of the feature is partly to blame for my problems, however; I really have a hard time associating Use autoscrolling with Clicking the MMB on anything but a hyperlink turns your mouse into a one-dimensional scrolling device, thus rendering it quite useless.

Phew, finally my middle button is free for use in, for example, Snap Links, which for some reason has ceased to respond to RMB clicks.