Calling River, in an effort to impeach the LaPage's testimony, was a mistake, IMO. Aside from appearing blatantly petty, her attempt didn't appear to me, to be successful.
For another, all Feldman has to do, is call La Page back to the stand to deny it ever happened (if it didn't happen, as River stated), or simply state that the medicine she was referring to was an over the counter pain reliever (as it may well have been). It is not uncommon for people to refer to over the counter remedies, as "medicine".