Did you design the InfoPath form from the SharePoint 2010 list using the Customize with InfoPath button on the ribbon? This works for me and I have 2013 InfoPath on 2010 SharePoint.
Or, did you design the InfoPath form in InfoPath Designer first and then publish? If so, please go to File->Form Options->Compatibility and make sure it's set up as a 2010 list form. Republish and retry. Should fix it.