Is the human body composition real?
No, it's only a very rough approximation.

I actually made a spreadsheet to figure this out.


The rows represent the composition as described by the quote.  I translated each into its appropriate chemical formula and converted all measurements to grams.  Then I found the atomic weight of each.  The gray area represents the grams of each element made up from that particular description, which are summed up in the first summary line.  The second summary line are the values as specified in The Last Word's link, which are based on a 70 kg (154 lb) person.

You can see that while some of the numbers are in the right ballpark, most are still off by significant amounts (the bottom row is percentage error - negative means the anime was too low, positive that it was too high).