You have done your homework by finding the Feigh case.  But you still can't finish the assignment, because it (purposely) left some questions unanswered.  It's an interesting opinion, though, and should probably be read by those who today are holding sacred every IRS "Notice."  For some background on Feigh, the low-income taxpayer clinic lawyer who represented the taxpayers has written about it here:

https://procedurallytaxing.com/invalidating-an-irs-notice-lessons-and-whats-to-come-from-feigh-v-c-i...

I haven't looked at Pub 596, but if it says "you may" and not "you must," then I would decline to exercise that option, leaving it out of the EIC computation, but advising the client that IRS Pubs are not sacred either, and they may get caught up in this controversy for years to come.