The child only had to hear the word once to be using it. Obviously it makes sense the parent is concerned and is wondering in what capacity the child came up with the concept. I think we would all be asking these questions if it were our child.
As mentioned state there is no tv in your daycare, you do not have any toy weapons etc. Ensure her you will monitor their play to see if you can pinpoint where the topic of killing has originated from and try to slip in that it is as simple as hearing it on the car radio, or over hearing the news etc. Maybe do this by noting that children this age naturally re-enact what they see and hear in a means to understand it so it could have been as simple as watching a Disney movie or hearing the news in the car.
By trying to naturally slip this in the parent may realize that even though their child doesn't sit and play violent video games they may indeed be exposing the child to this concept.
And yes, Disney is seriously violent!! I hadn't seen any movies in years and put one on while on mat leave and I remember sitting there rather shocked at how violent they are...and how I totally did not remember any of that from growing up watching so many movies!!