BurrMan is right, although initially I replicated everything Andrei did in his video. My first trim line was the same as his, and still I could not get a solid after blending the resulting surfaces; only a joined surface.

Then I cut through entire piece above and below the lip and got an acceptable result.

Hello,

The back edges of the original model are not fitting too well, rebuilding the base model from scratch leaves a better end result.

Good, understood.
I made new tutorial about Collapsing fillet (disappearing fillet). You can check it here:
http://moi3d.com/forum/index.php?webtag=MOI&msg=6058.30