The player is deinterlacing the film prior to sending it to the display, which is why you see 1080/50p. Whether that's better than the display doing it depends on the quality of the scalers in each piece of kit.
The Holy Grail for BD film-sourced video is 1080/24p. 1080/60p is something else entirely. It's when 2-3 pulldown is used to make the film's native framerate fit the display's native framerate. More often than not it's actually 23.976Hz to 59.94Hz rather than a solid 24Hz to 60Hz, but some discs are exactly 24Hz.
One imagines that some players have an 'auto' setting that just sends the native resolution and framerate of the content being played without upscaling or altering (my PC software BD players do this).