'HawthoRNe" Crew Says Jada and Marc Did NOT Hook Up

Multiple members of the crew that work on "HawthoRNe" tell TMZ ... it was clear to everyone that Jada Pinkett Smith and Marc Anthony were not intimate on the set.

The crew members we spoke with say ... they never saw anything inappropriate occur on the set. They add ... it seemed as if Jada and Marc went out of their way to squelch rumors. They would never run their lines together in their trailers but rather would do it out in the open, with an acting coach present.

And 3 crew members noted that Will Smith would sometimes come to the set while Jada was filming and, as one of them put it, "It looked like they were on their honeymoon." No one we spoke with saw any conflict between the two.