I was unable to repro your issue on my end.

Below are the steps that I made during my attempt to replicate your issue.

1. Create a test page (the test page file is attached) of WebInput.
2. Set the “CultureName” property of WebInput to “it-IT”.
3. Enable “DisplayFormat” of WebInput and set the “Format” to “dd/MM/yyyy”.
4. Set the “Current System Locale” of the tester computer to “en-US”.
5. Run or view the test page in browser.
6. Click the drop down button to show the date time picker.
7. Select a date, for example: Mercoledì, 02 Giugno 2010 (Wednesday, June 2nd, 2010).

WebInput shows the selected date as expected, “02/06/2010”. I enclosed the test page as attachment. Please let me know if there is anything that I miss during my attempt to replicate your issue. You may also modify the attached sample if you have different scenario.

For your information, I use WebInput 4.0 build 1 and WebUI.NET Framework 3.0 build 750.