This should be relatively easy to clear up by checking the roles and responsibilities for her appointment in the company. Whilst I agree with the message she broadcast, if she did abuse her credentials to make it, then that sound to me like grounds for termination.
"I created a little notification, only a few lines of code, that pops up in the corner of the browser whenever my coworkers visited the union busters"
tbh, the way she qualified this statement with amount of effort involved puts me in a mind that she knew she shouldn't have been using company time for this endevour.