Sorry, guys.  I'm actually using Blender 2.73, not 2.72 as I indicated in the title.  My mistake.  I did a quick search for inset bugs in Blender, but nothing about this turned up, so cant figure it out.  Only seems to occur when I am working on an object where manual edge loops were inserted, and a subdivision modifier exists on top in object mode.  Otherwise, inset seems to work ok.

Edit:  Nope!  I was wrong!  It does the same thing!  So this seems to only occur after edge loops are added with the Loop and Slide command.  There's no subdivision modifier on this cube.  All I did was add some edge loops first, then selected the four faces, and inset.

Same strange edge triangulation issue.  That's a pain in the butt!  I'm starting to wonder, however, if this is a bug with Loop Cut and Slide, and not Inset?  WTF?  If I select those extra edges, click X, and delete edges only, the entire top of the box gets deleted, but the cross section of edge loop segments I added with Loop Cut and Slide still remain!  Very strange topology behavior.

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Tools :  3dsmax 2015, Daz Studio 4.6, PoserPro 2012, Blender v2.74

System: Pentium QuadCore i7, under Win 8, GeForce GTX 780 / 2GB GPU.