Well no, they still kept the basic dimensions and mechanicals. But the bodyshell is otherwise totally different in design and construction, the bogies are totally different, the doors are totally different...
I agree and in actual fact they don't share the same dimensions either. The 158 is not the same size as either a Mk3 coach or a Mk3 based DMU/EMU.
I would suggest that if BREL had won the contract for the Mk4s that they might well have been aluminium construction like the 158s.
I believe the 158 construction was based on work done on the APT-P which was also made of aluminium extrusions. This design refined then into the Networkers, Electrotars and Aventras.
A family tree
BREL: Mk3 > Mk3 EMU Mk1 (455/317) > Mk3 DMU (150) > Mk3 EMU Mk2 (319/320/321/322)
Met Cam: 156 > Mk4 > Coradia/Juniper (170, 334, 458 etc)
BREL: ATP-P > 158 > Networker (465/165 etc) > Turbostar (168, 170, 172) > Electrostar (375, 377, 387) > Aventra (345, 710)