The problem happens after the patch face is internally triangulated , when deciding which triangles are filled vs. holes. Try the following:
dt = delaunayTriangulation(poly);
text(poly(:,1), poly(:,2), cellstr(num2str((1:size(poly,1))')), ...
'Color','m', 'HorizontalAlign','left', 'VerticalAlign','bottom')
You can see that the triangle (2,3,4) corresponds to the one not filled in your example...
A simple workaround is to nudge the coordinates of the shared vertex 8, e.g:
poly(8,2) = poly(8,2) + 1e-6;
The offset is too small for you notice, but it should fix the bug for now.