The parameter for the v2 data API is "author," not "authors." Unfortunately, fixing that won't solve the problem, as the retrieval of videos from a particular channel can only accept one author at a time. This is also true for v3 of the API.
The reason behind this is that the comma is treated as a concatenator, looking for a video that was published on FoxBroadcasting AND ABCNetwork (the use case for having multiple authors in that parameter is if you are retrieving activity feeds, in which case you want both feeds so having the comma serve as an AND is correct).
So for now, the only solution is two separate calls.