Jesse Showalter -- the attorney for the deliveryman who was detained and later released in the Nancy Guthrie investigation -- tells Emmy-winning journalist Brian Entin his client endured at least 5 hours of questioning for no good reason.

Remember ... a man named Carlos Palazuelos -- who works for DoorDash and GLS -- was detained by authorities about 60 miles south of Tucson, Arizona. Law enforcement also questioned his family and allegedly broke down their front door while raiding their home.

Showalter tells Entin that Carlos was handcuffed in the back of a cop car for his 5-7 hour interrogation and still hasn't gotten his cell phone back from authorities.

What's worse ... Showalter suspects they had no just cause. His best guess is that they were acting based on some "electronic evidence that is really dubious," like "cell phone pings" or "flock cameras."

Showalter says, "I don't know that he was ever even in that area."

According to the Pima County Sheriff's Department, their search was court authorized.

As you know, Nancy was reported missing on Sunday, February 1 ... hours after her family dropped her off at home following Saturday night dinner with her daughter Annie Guthrie and Annie's husband Tommaso Cioni.

All family members have been cleared from suspicion in the case.