It seems I understood the water heater (smaller BTU appliance) should connect above the furnace.
This has apparently been this way since day one. I’m not even sure if they even connect to a pipe inserted in the chimney, or are just using the chase, (couldn’t mount the roof).
My CO meter says it’s okay, and both appliances seemed to draft okay.
Should this be recommended a HVAC tech switch this any way?
Were they gravity exhaust appliances or one (furnace) fan induced draft?
http://www.nachi.org/forum/f20/water-heater-exhaust-location-furnace-and-masonry-chimney-60751/
http://www.ashireporter.org/HomeInspection/Articles/The-Word-Common-Vent/2328
Typically, the smaller btu unit needs to vent into the chimney above the larger btu venting unit.
Do not common-vent natural draft with appliances that use a positive-pressure draft.
That was another issue as well, Larry. The furnace is fan induced draft, the water heater is natural draft.
Just because you run with scissors doesn’t always mean you will lose an eye 
I suspect that 9 times out of ten or maybe even more than that, incorrectly vented gas appliances still work OK without producing CO or killiing anyone, having said that people die every year because of CO.
What’s in your pic is super easy to fix, plug the little low fella and put a tee for the water heater on the high large big pipe.
Refer it to a qualified person, that is why they asked you to do an inspection, to find what is wrong.
Well put, Erik, that’s exactly what I told my client, except I said use a wye, or better yet, use a qualified HVAC Tech. 
If they are on separate flues it does not matter and since you have no idea forum guys will not be able to help much here other than quote the obvious.
You maybe could have looked for an old cleanout.
I suggest you get a telescoping rig for next time as it will only set you back $50.
At this point you can list a definition and explain that termination was not observed.