I have a thought based on piecing together two bits of information.
One is that the identity of Dean's wizard father is unknown. We know that he left Dean's Muggle mother when he was young without telling them about the Wizarding World hoping that it would protect them during the First Wizarding War. We also know that he later was killed by Death Eaters when he refused to join them.
The second is that there is a caveat in the description of the Shacklebolt family, that Kingsley Shacklebolt is the only member still alive, at least known to the Ministry.
I think it's worth considering that Dean may be an offspring of the Shacklebolt family.
Supportive facts: The Shacklebolt family was pureblood, one of the Sacred Twenty-Eight. Being a member of one of the families would be attractive to Death Eaters, something that made you potentially recruit-worthy. A member of the Sacred Twenty-Eight having a Muggle wife and half-blood son would put them in danger if the Death Eaters were to know about them. Consider Voldemort's order to the Black sisters to kill Nymphadora Tonks.