OK now for the real answer. The only proof of ownership is a sales receipt. Breeders/owners often sell dogs without registration papers, but are usually happy to show/give you the pedigree. Nothing on earth would be able to stop you breeding from her other than if she had already been spayed, you just would not be able to register the pups with the KC, so this is probably what they are trying to do.
Any person who breeds/owns a KC registered dog can WHILE THE DOG IS IN THEIR ACTUAL POSSESSION place an endorsement on the registration 'progeny not eligible for registration' but this cannot be done once the dog has left their possession, so unless this is already on the registration it would be too late to do it, unless you signed an agreement saying you knew this was going to be
put on. Without this agreement or if the endorsement was not already in place the KC would agree to you requesting them to remove the endorsement.
So I would say go ahead if you are happy to take the bitch on without wanting to register any puppies. I would say though that if you are trying to get a cheap dog for breeding then think again, because any reputable stud dog owner would not let their dog be mated to a bitch without papers, and you would find it difficult to sell unregistered puppies unless they were very cheap.
I hope this helps. I would also find out why they are parting with her, and whether they actually bred her or bought her from a breeder. If the latter I would suggest you contact the breeder to let them know you have her and she has got a good home (hopefully!). Most reputable breeders want to know where their pups go.
One more thing, be prepared for lots of slobber, on the walls, on the tv screen,up the fridge door, in fact anywhere they can project it!