> The fingerprints of twins are not more similar to one another than that of two random people.

That’s not accurate. Family members have more similarity in their prints than among random people, twins even more similarity, and identical yet more.

I can’t immediately find authoritative references for family and fraternal twins, but here’s a reference for identical twins:

“Identical twins have the same chromosomes and similar physical characteristics and, therefore, they have a high class/type similarity in their fingerprints.” https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3338710/