Chris,
I think what you say, no unsecured PSLs, must only apply to Cabair as Oat students can still get them up to £25K. The bank's criteria will be higher, as is the interest rate, but the Oxford branch will consider doing it for those with good employment/earning records.
If nothing else, this thread should show that one needs to choose where they will train and then discover the financing options specific to that FTO.