I am confused, the quality of your camera really has nothing
to do with it.
You can have the best camera in the world - but if the green on the costume is similar ENOUGH to the green in the chroma cloth, then yes, you run the risk that the green will be keyed out along with the backdrop; unless you have a great backdrop and lighting, you're going to have to key a range of greens out (this is what you're changing when you alter the black & white points of the key settings).
However, to preserve the green sections of the actor's costume, you can simply apply a freehand animated garbage matte around those sections if any of them do get keyed out. I've done this in the past, and it's usually a quick and easy process, as the mask doesn't need to be hugely accurate.
I hope this helps