That is very true. Your puppy cannot give you rabies if it doesn't have rabies, and has not been bitten by, or in close contact (exchange of saliva/blood) with another rabid animal.
But as soon as you can, do take your puppy to a vet for the usual puppy shots to protect it against developing rabies in future.
You are not going to die of Rabies if your dog does not have Rabies. Just keep your wound ckean and wash with soap and water if you can.