So, here is the position, the end of a line that the computer analyzed and suggested.  

I kid you not..

It's mate.

Well, duh! After the obvious move Kxc1, White's up tons of material. How could you not see that?

(I'm kidding, for any readers who don't realize it)

That is checkmate...

Yes, that is why I'm confused as to why the computer would say "What has a decisive advantage".

It isn't bonkers.  The chess.com computer analysis has what is called a "horizon" problem.  (the computer only looks so far).  I would strongly suggest another mode or legimitimate program for analysis (Rybka, Fritz).  It is of concern though because members pay for analysis and not some variation that spits out checkmate.  I've complained about this before.   I wrote about it here

http://www.chess.com/forum/view/help-support/analysis-spits-out-wrong-variations