Answer:
A quitclaim deed is actually very risky in this case. The alleged owner will sell you the property but if anyone else (the cousins maybe) makes any claim on the property and their claim is valid, then you will have to pay them money. In this case it is a gamble really, if the cousins do not make any claim, then you got a great deal, but if the cousins make a valid then you lost a lot of money. Is it really worth it? I doubt it. When a deal is to good to be true, it is actually not a good deal at all.
On the other hand, a warranty deed will provide you protection against any possible claim from any third party, including cousins, any other type of relative, mortgages, delinquent taxes, etc. A warranty deed protects the buyer and any possible future claim must be settled by the seller.