The company that I worked for had a written policy of not allowing any type of screensaver, program or application on its system without receiving approval from the IT section. If management explained that was the issue with the screensaver and she refused to remove it then it would be grounds for dismissal. What I would be curious to know is whether any of the other employees have personal screensavers or photos of a relative, pet or vacation trip on display that aren't on an approved list.
Upon further research I found this article in the Boulder Daily Camera. It appears that there weren't any issues with other photos that she had used as wallpaper backgrounds. It doesn't appear that it was an issue with computer security--she even had a photo of her wife as wallpaper at one time, but rather the display of the LGBT flag (ETA: and that someone was offended by it).
BCH issued a statement on the situation Wednesday.
"An employee recently resigned from her position related to use of a shared workplace computer and a dispute with a coworker," the statement read. "The employee who resigned was never threatened with termination by any member of the management team or Human Resources Department at BCH. The employee was offered the opportunity to have formal or informal mediation with her coworker but declined that option and chose to resign."
Hurn, who has been with BCH as a clinical dietitian for a year and a half, said it all started about a month and a half ago. Her office is not in a public patient area and only a few people have access to that wing, but someone saw the screen saver through her office door and complained about it to Hurn's supervisors, who ordered her to delete it.
"It was really hard, and really terrible," Hurn said. "I never asked for any type of special treatment."
Hurn said eventually someone just went in on Hurn's day off and deleted the screen saver off her computer. Hurn said she pleaded with her supervisors and BCH's human resources department, but got nowhere. Finally, Hurn said, "I'm done. I felt like this has to stop."
http://www.dailycamera.com/news/boulder/ci_30704159/boulder-hospital-employee-resigns-after-being-told-delete