How do you handle and prevent Responsibility Drift in your organization?

As new technology pervades all departments within an organization, there is a tendency for non-technical managers to resist owning processes related to their own department on the grounds that it has a technical component and should therefore be an IT responsibility. For example, IT introduces a way to automate data cleansing – the Data Entry manager now believes IT should be responsible for the correctness of their data. Or a new feature is introduced on the company web site – the Customer Service manager now wants to defer customer questions to IT. Have you experienced this in your organization? How do you handle and/or prevent responsibility drift in your organization?