I thought like you, that the AKC required any dog siring 3 or more litters to be DNAed. I couldn't find a number on their website. Maybe I wasn't looking in the right place, tho.
From the AKC's website (italics are mine):
DNA Requirements
AKC DNA Profiling is required for: Frequently Used Sires (dogs having the greatest impact on the AKC Stud Book); imported breeding stock; dogs whose semen is collected for fresh-extended or frozen use; and for the sires, dam and puppies for Multiple-Sired Litter Registration.
From the AKC's website (italics are mine):
DNA Requirements
AKC DNA Profiling is required for: Frequently Used Sires (dogs having the greatest impact on the AKC Stud Book); imported breeding stock; dogs whose semen is collected for fresh-extended or frozen use; and for the sires, dam and puppies for Multiple-Sired Litter Registration.