Hi,
Has this mom been using any soap, lotions or potions on her breasts?  Does
she have maybe a dermititis condition?  Yeast?  Any of these can cause
bleeding of the nipples/areolas without friction from the breast pump.
Regarding the suction power of a rented pump vs the hospitals pump, the
suction and strength should be fairly equivalent.  I have seen no real
difference in suction strength between the Medela Classic (Hosp grade) and
the Lactina, and I have used them both.  Now I know nothing about Ameda, so
there may be a difference there.

Good luck!
Jay