The issue is that in this case, if the co-worker really is so ineffective, it shouldn’t be terribly difficult to find the quantitative data. If she is rude to co-workers on such a wide scale then I’m sure that either her supervisor or HR have received complaints. If she is lazy, then her supervisor should be able to look at her productivity levels and decide if they are on par with other employees. Why is the DUmmy so concerned with getting her fired in the first place? If she is really so bad, start reporting every major incident to a supervisor, and if they are valid issues, then there would be a record in place to get rid of her.
Firing somebody because they appear to be slothful, without the evidence of poor work performance would be stupid, and could set the company up for a lawsuit if the employee wanted to pursue it. Maybe it looks like she doesn’t do as much work because she is faster at her job, so it doesn’t take her as long.