How can I make Grid parse non-default dates?

I am using Grid widget to edit a DataShape that contains dates. This works fine as long as I display the dates in their default format - dateTimeFormat_Default, as chosen under Configure Grid Columns.

However if I change the date format to e.g. dateTimeFormat_MediumDate then any edits to the date cause it to break. If i edit the date - even in a simple way, like changing the day number by one - the contents are not parsed correctly, and a nonsense or invalid date is entered into the output dataset.

How can I fix this? Is there some way i can tell the Grid how to parse the dates i give it?