The only thing you can't patent is a live human being or a mental process. Everything else is fair game.
There has been an enormous row over for instance the patenting of basmati rice, a staple food in many countries.
However, I would be REALLY hesitant to conclude anything from this other than Celera chose uninteresting things to make patent applications on. The "outcome" for innovation in this study was whether or not a gene test exists, and that is not what Celera was trying to get IP on. They were trying to find drugs or drug targets - and that is a difficult process.
The fraction of good drug targets in the human genome compared to the total number of genes is very, very small.
Which, incidentally, is why you shouldn't be able to patent testing for single genes, since that is the most rudimentary example of what genetic testing has to offer.