The cancer that he had was clearly his own, as evidenced by the fact that they were able to match up his normal genome with the tumor genome and find the handful of differences that were driving the cancer.
*Full disclosure: I work in the Genome Institute at WashU, where this sequencing was done, and while I did not work on this particular case, this sort of cancer genomics project is what I work on all day long.
The reason tasmanian devils can transmit cancer is that they're not genetically diverse enough to differentiate foreign cells from their own cells. But that's the exception that proves the rule: tasmanian devils are unusual in that they went through recent population bottlenecks that dramatically reduced their genetic diversity.