SharePont 2010 - Why is Inline Editing not working even when enabled for the current view?

One of my colleagues at Oakton had issues in that a SharePoint 2010 Custom List wasn't allowing editing inline.

Even when modifying the view and enabling the "Allow Inline" editing property of the list view - no errors, it just didn't work and the Edit icon just opened the full blown SharePoint modal dialog box as usual.

The problem was that the list view must use the Default Style for Inline editing to work.

DDK