Shouldn't a diagnostic test be done before putting a new radiator in?

Actually the proper testing and diagnosis could not have been performed with a failed radiator .. The engine would've needed to be running at normal operating temperature and the cooling system full of coolant before accurate testing 'could be' performed.. This is unfortunate but it does happen quite often, after one repair has been made, other problems often show up as the vehicle can be operated for further testing 'after' the original repair BUT it could NOT have been 'before' hand .. You can always get another opinion on what is needed to make the final repairs .. I hope this helps... Good luck with it!