Thanks for that explanation, but I am still somewhat confused why that would be. In the case of mining multiple chains with PoC, there is not a "Nothing at Stake" problem that I can see. If you mine on 2 chains, you have to devote capacity resources to 2 chains, splitting how much you can earn. Only 1 of these chains will eventually win, and then all the value you earned on the second chain is lost.
The NaS problem arises not on 2 separate chains, but on different branches of a single chain. If two blocks at the same height are found on top of the current block with the most work, then in PoW you must split your computing resources to work on both branches. But on PoC there is negligible cost to extend both.