would have vs would have had

According to the "Hokke denki", Wu Long was a believer of Taoism and he hated Buddhist teachings so much that he ordered his son Yi-Long not to write the Buddhist sutra as his testament or he would have had to face big problems.

The above is from a Buddhist magazine.

A friend of mine said would have had is wrong and that it should be would have instead, but I think otherwise. However, I'm unable to explain to him why he is wrong. If I'm right, could someone please explain to me why "would have had" is correct ?

Thanks.