After spending some time with the Atmel SMART E70 datasheet (dated 19 Jun 15), I might just as well share my findings with you:
I could simply not start anything else but TC0, channel 0. The reason turned out to be that each channel has its own peripheral identifier (PID23-28 and PID47-52).
I e, there is not one PID per module (TCx), which one might think when reading p. 1355, where the IDs for the interrupts are listed.
The same PID is supposed to be used for both PMC and INT according to p. 258, so I am inclined to believe that the information on p. 1355 is incorrect.