The external seams perhaps simplified welding a bit whilst the production engineers worked out a more elegant solution.
Minis were produced on new Longbridge lines which had been making Austin A35s. It was intended as a multi purpose build system, and several models passed along it. As many BMC owners remember, it incorporated an effective rust proofing process. From memory, the only external seams on an A30/A35 are the roof line and drains (common practice) and sill bottom. That was a car designed six years or so before the Mini, so we can assume that the plant did not require external seams. It is more likely that production was rushed -- one underfloor seam on early models opened the wrong way and collected water as the Mini drove along.