I have often seen elk and cattle in close proximity to each other.
For the past 10 or more year I have watched a herd of up to 150 elk summer in the fields below my house. The elk are usually in fields without cattle, but sometimes they are in the same field.
One time I was bow hunting in the oak brush of NW Colorado. I could hear large animals feeding in the brush ahead of me. When I finally got into an opening where I could see that they were cattle, I stood erect and said something like "Oh, stupid cattle" and a dozen elk broke from the brush around me and ran off.
A friend of mine used to be the Montana F&G biologist for the Wall Creek elk management area south of Ennis, MT. He once told me that he found that if they put cattle on the range early for a month or so, it would actually improve the feed for the elk later in the year.