As a member of the UHS 2002 class, I can tell you that the only thing that steered people in my class into primary care was their own personal choice of going into primary care. Absolutely no one that I know off had any trouble matching into a non primary care field, and at very strong programs too (Mayo in Rochester and FL and the Cleveland Clinic to name a couple of the better known).
During my 4 years at UHS, there was never a single time when I felt the school was trying to convince or pressure us into choosing a primary care specialty.
Although I hated a lot of the politics at UHS, I feel I got excellent training there. If you stay out of the politicking (and all med schools have that, it is not a "UHS exclusive", although it seems that DO schools have a greater share of it than allopathic schools) you will be very happy with the education you will receive at UHS. Not to mention that the facilities are state of the art and KC is a very liveable city.
I cannot speak about UNE but I would choose UHS again if I had to do it over (thank goodness I don't 😀 , being a medical student once was more than enough!)