But (my bio is rusty) a haploid genome (gamete) cannot fully represent the genome of a diploid human.
If you're looking for genetic disorders, these will often be the result of recessive traits, right? So having only half of the chromosome sets is not indicative.
That's my example of hair color. With a full genome sequence, you could determine the person's hair color, but with a haploid genome, you could not.
If OP's joke is about the privacy implications of sperm donation, then saliva seems more risky.