Earlier quoted context omitted.
Well, except they don't split the water, but the urea contained in the urine. Now, I don't know whether that process takes more or less energy than you gain by burning the end result, but it's not the same process.
You can't electrolyze urea by solving it in water and passing electricity through the solution, for that you'd have to melt pure urea and electrolyze that. Problem is that it will decompose above its melting point. So, even when urea is solved in the water, only the water is electrolyzed (in hydrogen and oxygen).
[1] see https://en.wikipedia.org/wiki/Urea#Laboratory_uses
Edit: There are papers about direct electrolysis of urea
http://www.suttonfruit.com/pics/urea_electrolysis.pdf (I think its a copy of http://pubs.rsc.org/en/Content/ArticleLanding/2009/CC/b90597...)
http://etd.ohiolink.edu/send-pdf.cgi/Singh%20Deepika.pdf?ohi...
Now I don't know how legit they are, but seems ok to me.