comparative construction used with pronouns, especially 'her'

I was recently pulled up by a colleague when I made a statement along the lines of I am a better player than her. My colleague suggested the correct statement should be better player than she is because her is a possessive pronoun, and my colleague was waiting to hear what noun her referred to.

I was unconvinced. I am able to say:
I am taller than Jim, which can become I am taller than him.
So, just because her is both the feminine possessive and personal pronoun why does that exclude me from saying I am taller than her?

Or, have I made a false assumption, and should never have a noun/pronoun without a verb at the end of a comparative structure? Should I always have been saying I am taller than Jim is, and Rabbits are faster than turtles are? This seems awfully cumbersome