Well then she should appeal the written warning. The company should have a process for doing that - it ought to involve someone (or more than one) having a look at the process, the evidence, and the decision based upon the evidence. One cannot introduce new evidence.
Just a final point. It's a written warning we are talking about here - not a final written warning or a dismissal. This is a second stage of a disciplinary procedure (using the first stage might have been a verbal warning - some companies don't do that stage) so I would merely suggest being circumspect about the amount of pain a grief she goes through in pursuing this. Firstly it is potentially stressful for her. Secondly, what outcome is she wanting? - 'clear' her good name presumably. Sometimes it is just better to lie down and get on with life. I appreciate this is a dangerous thing to say to you, so I back it up as follows. Having worked in HR for a number of years, there are those staff who can be relied upon to be a pain in the arris, always know there rights and always seem to be obstructive of what management want to do. Some are interested in seeing that the process is fair, that they have had their say - true socialists perhaps. I can have a certain respect for that.
Others are just out to get what they can for themselves, throw sickies and run a fine line between just avoiding to be dismissed. You can be sure that some HR departments seek to look for a 'gotcha' for such people when they push the boat too far. That's human nature, I feel.
I am not passing comment on which category your gl falls into - merely that sticking one's head up above the parapet tends to get it noticed. After 12 months or less, a written warning just disappears.