I totally agree with the color graphics.  I have encountered situations like this with my clients and even on my own hair.  Black is a mission to get out...but I have found that it can be done...you must emphasize to your client that they use some sort of treatment on their hair perhaps even come in fore a few conditioning treatments.  And I always find it helps to clarify their hair under the dryer first before I got to do any color correction.  Clarifying works great as well if someone is on medication.