You really ought to replace those sills. As well as the corrosion trap, if they are welded along the lower edge, the structure is not nearly as stiff or strong as in the proper arrangement, where the welds are near the base of the inner sill, forming the box section properly. The flexing which results is one of the reasons why the corrosion happens so quickly.
I won't be replacing the oversills, they are brand new and were fitted professionally before I purchased the shell. Some people just have a preference; a friend of mine has been working on mini for years and knows them inside out. On the mini hes working on at the moment (which hes spent about 10k on) he has fitted oversills, spoke to him about this and he said if they are waxoyled properly and regularly they will be fine, and wont rust any quicker than vented sills.