I should have mentioned my experience with computers before explaining the problem. I until very recently was a laptop technician. I have moved on to a position in a church as an IT technician.
I would tell them that you have heard that this could be a problem with the display itself or the cable, and tell them that you would like them to check that very well the insure that there is no problem with either of them. I really don't think it is the video card, but still is possible. I would also move the screen forward and backwards to see if it is the cable and there is a break in there so you could duplicate it on and off as 100% proof there is a problem with the cable.
Let me also try to somewhat explain the fix it or replace it policy apple has, I have been dealing with multiple repair attempts before with a common issue.
There is really three possible levels of repair/replacement, you start on the bottom. The "Fix it", this really only applies to software problems, they will repair any problems that they find. This is a labor only cost to them. The second level is "Replacing parts", this is a very popular repair on many different brands of computers. Most electronics made today are mad up of many smaller, cheaper, easier to replace parts; this could be anything in the laptop, the logic board, the screen, hard drive, etc. Then the final level of repair is the "Replace it", this is not very common to have done, and they really don't want to do this. Apple's "written" Policy on repaving the system is it would be exchanged for a new system within the first 2 weeks. Apple's "unwritten" policy on replacing the computer is that if during the length of the warranty, if a problem with the hardware arises, and is repaired unsuccessfully 3 times, they will swap it for a brand new current model. What does this really mean, lets say your video card fails, you take it in for repair, once repaired everything works fine for a while, then it happens again, this happens 3 times, then on the 4th time you bring it in this policy can kick in. Note since this is unwritten, it can happen, there is no guaranty it will happen. But what I have heard is if you are nice and understanding to them and express your concern for this repeated issue, they will consider it. On the other hand if you walk in there throwing a fit yelling and screaming, the will not want to help you out. They do take notes on everything that goes on during your appointments and they will look back at them during this time.
I hope this helps you understand their fix it, or replace it policy a little better.