The pilot did not mention a third crew-member when asked by ATC whether he was single-pilot, he simply said that the injured crew-member was fit to perform his monitoring duties.
That's a little odd. In my opinion, if there are only two pilots available and one is unfit to be pilot flying by virtue of an injury, that is a single-pilot operation, no matter how much 'assistance' the injured pilot could give in normal operations.
In our airline, if a pilot were to pass out but recover, apparently fully fit to continue, a Mayday and diversion would still be required - just in case.
Naturally, I know what I'd do and I am conscious of what common-sense dictates in these circumstances, but rules is rules...