innjan
This isn't an area we deal with on the forum so I am limited on the advice I can give, but from what you have posted I'm not sure that the DWP and the college are providing incorrect advice!
With regard the Bursary, it will be treated as income for the UC and may be deducted from it. I can't say whether this would be in part or in whole but I see no reason why the bursary should be withheld simply because she is receiving UC.
As to the UC, the requirement is that she is receiving PIP
and she has Limited Capability for Work, your post suggests that she is still being assessed and may only being treated as having LCW. It is worth checking whether this will be a problem or not.
Have a look at t following for more information
www.disabilityrightsuk.org/how-we-can-he...d-questions-students Gorodn