Mike Vrabel and Dianna Russini

Mike Vrabel and Dianna Russini are doing their best to put out the massive fire that erupted after they were spotted holding hands recently ... insisting the pictures published on Tuesday don't tell the real story.

Page Six obtained images of the New England Patriots head coach and Athletic NFL reporter -- who are both married to other people -- spending time together at the Ambiente resort in Arizona when they were in town for NFL meetings last month ... showing them lounging by a pool and hugging on a rooftop.

The outlet also cited sources claiming the two were damn near inseparable throughout the day -- enjoying breakfast together before hopping in the hot tub ... and then soaking in the sunset later that night.