To reproduce, you can change the column headers of http://datatables.net/release-datatables/extras/ColReorder/theme.html like this:
The table is nicely initialized with jQuery UI theme. Now call (eg. in your Firebug console):
When DataTables remove the JUI classes, the selector should be "th, td" (or maybe the nodes have to be marked as "modified by datatable" to not remove the JUI classes if they are in the original markup)
The new API has this in it: https://github.com/DataTables/DataTables/blob/1_10_wip/media/src/api/api.core.js#L109 .
Wow - 2 years. That must be some kind of record :-(. Sorry!