I noticed while I was fiddling around with it that the brscan4 package file I had was
which clearly isn't right since I'm running 64-bit. I went to the Brother site and saw that the (red) visited link was indeed to the 64-bit version, but that the links to 32 and 64 bit were reversed in order to how they were everywhere else on the site. So, suspicious, I went to the 32-bit package link to see what it would give me. As I suspected it gave me
So I uninstalled everything again, reinstalled them (with the right brscan4 version this time) reran brsaneconfig4 and brscan-skey. Just to be safe I linked the files that now existed in /usr/lib64/sane to usr/lib. i.e.
Now everything works. So, check which files you've got! The links on the Brother site for the brscan4 packages are reversed and don't go to the files they say they go to! So I've sent a support e-mail to Brother telling them about this mix-up, so hopefully others won't have this problem. I'll mark this thread as SOLVED.
root@kinetic-poincare:/usr/lib# ln -s /usr/lib64/sane/libsane-brother4.so .
root@kinetic-poincare:/usr/lib# ln -s /usr/lib64/sane/libsane-brother4.so.1 .
root@kinetic-poincare:/usr/lib# ln -s /usr/lib64/sane/libsane-brother4.so.1.0.7