No, cops, crime scene specialists and forensicists wear gloves when they collect and handle evidence. Each item is photographed where and how found, then collected, bagged and labeled and numbered before going to the next item.
It is against federal law to submit DNA profiles to CODIS from individuals who voluntarily give a DNA sample, and it is not supposed to be submitted to any state record system, either. In this instance, "voluntary" means it's being submitted for purposes of testing for just the case at hand. "Voluntary" does NOT mean voluntarily submitting to retention of your profile, once excluded from the case at hand, for any future reference.
If a cop was found in the professionally embarrassing position of mishandling evidence such that he needed to submit a DNA sample, he'd probably hear from at least a captain about it and would be severely razzed by his brothers. His DNA profile would not be submitted to a database.
So why was the head of the lab's DNA on the evidence? He doesn't wear gloves? How did they know it was his?