What app is it? At least for me any app that uses push has it's own setting to turn it off. (Though some seem to turn back on sometimes, perhaps after updates) Btw it may not be obvious at first. Just as an example, a weather app that gives the temperature on the status bar is using push. To turn off push, there may be no push setting, but instead you turn off being notified in the status bar and that in turn stops the app from getting information on it's own.