No human with ovotesticular DSD or any other DSD has "both sets," though. That's true whether you're using "both sets" to refer to gonads or to the external body parts commonly known as the genitals.
People with DSDs are male or female just like the rest of us. The fact that some individuals with DSDs have ambiguous or atypical physical characteristics that mean some extra investigations are needed to determine for certain which sex category they properly belong in for medical purposes - and for areas like competitive sports - doesn't mean they aren't male or female.
It also doesn't mean people with DSDs are a hybrid of both sexes like you contend. Even people with ovotesticular DSD can be slotted into one or the other of two sex categories in the situations when it's necessary to do so.
The existence of edge cases doesn't undermine or refute the fact that there are two sexes.
Also, trying to make people with DSDs seem so totally different to rest of us by spreading the falsehood that some DSDs make people so physically peculiar, perplexing and utterly unfathomable that they can't be categorized as male or female - and by using the offensive, dehumanizing term "hermaphrodite" for them - just makes the lives of people affected by DSDs more difficult than it has to be.
Living with a DSDs or having a child or other loved one with a a DSD is hard enough as it is. Spreading misinformation about DSDs in our species and the people who have them like you're doing only sows more confusion and serves to stigmatize, other, "monster" people with these rare medical conditions.
You're also not helping shed light light on DSDs, or showing compassion for the families affected, by the cavalier way you speak about the cruel past practice of doctors in the Western world operating on babies and children with DSDs - "snip snip" as you put it - under the false premise sold to worried parents that some children with DSDs "can be changed [from] one to the other" sex and that their atypical-appearing but otherwise healthy reproductive organs require some kind of"medical solution" or "fix."