Thank you. I am sure that if LE has the photos, we're all just playing catch up. But it's good to see what we can find.
I think I'm now 100% about that being their group, and the photo was taken at that time. I don't see the cloud definition in any other period that looks like the clouds behind Alex. You can see in the very top left here in this video where the camera lens would have picked up the clouds with light breaking through just enough. Too much earlier and it was just misty and foggy. Too much later, you have rain. This portion of the video is at 11:19 a.m. (Go to 15:49 in the video)
ETA: Then there's another group at 16:56-17:09 that match as well. Thankfully not very many groups of 4 there that day with one shorter kid. The clouds behind and the direction the wind is blowing the steam behind Alex is almost exact. So...I prefer this second group. But either way, this puts them at East Chinaman Spring between 11 and 11:30. If they were there for Old Faithful, they just missed it at 11:05, unless they came from there. Then there's hours and hours to get to many other places in the park. Norris Basin again is not far from Old Faithful nor the entrance at West Yellowstone to get home afterward.