Post # 25 by PEI 3721 is worth a read; it mentions a couple of areas of interest, worthy of a revisit, research and ponder. Just thinking out loud here and trying to get a positive fix, not on went wrong, but why.
Once the turn onto the ILS is made, the last thing needed is any sort of doubt about 'Who's on first' and 'What's on second', early in the piece there is time, not a lot, but time and space are available to determine 'what's wrong with this picture'. I expect most have been in the position, a little high a little hot, vectors, radio, turbulence, ice, cramped for wriggle room etc. and being a little 'untidy' on the intercept, all easily sorted; but, what if the 'expected' picture goes pear shaped. These guys had two separate 'mental pictures' ~ expectations, to unscramble, with doubt, disbelief in the mix. Something was wrong, but it seems they were unsure of exactly WTF was wrong, now that's scary. The doubt, disbelief, the urge (if you like) to sort it out, within a sane time frame, would be strong; before giving it away. Remember the Dash 8 CFIT, the one that had the undercarriage problem, the attention of both crew focussed inside.
It's so very easy to say they should have gone around and I agree; being unable to know what to trust is reason enough; however, they did not. The elements which preceded the attempted late, rather than early overshoot are of interest, starting at just before the turn onto final. More reading and head scratching required methinks.