Here are the additional steps we took to figure this out: (spoiler alert, there is no concrete explanation)
1. Other draftsman (#3) opened same drawing (we all share files from central location) and could NOT see the point IDs either on his machine.
2. This draftsman deleted the points and re-imported them using MAPIMPORT. Now he could see the IDs.
3. Original drafter (#1) came back from lunch, we asked her to show us how she imported points. In Map (planning & analysis) from insert tab, she selected MapImport. Brought in points (I was checking to make sure she had selected the add data option, I was sure this was missed) but she did it correctly. When she checked the points, she could NOT see the ID.
4. I opened the same drawing on my machine, could not see the point ID. I deleted and re-imported the, using MAPIMPORT (from Civil) from command bar. I could see the point ID. I saved this drawing.
5. Original drafter (#1) opened the drawing I had just saved and COULD SEE THE POINT ID. The problem was not with her properties box settings.
6. Finally, she deleted the points and re-imported them using the MAPIMPORT command from the command line instead of tool bar, the way I did. Now she could see the point ID.
Conclusion: There may be a glitch with importing from the insert/mapimport tool bar. She did shut down AutoCAD between steps 4 and 5 so the restart may have fixed something. I have run out of energy to check again to see if her initial import method (from toolbar) was the problem but I have used that method many times with no issues. My guess is that restarting her AutoCAD fixed some kind of bug.
Thanks for the input and hopefully this helps someone else in the future. Ugh what a waste of a day.
Have a nice weekend!