Everyone gets an A for effort on this. But what amazes me how you're able to diagnose the problem, better yet, tell someone not to worry about it, from such a DISTANCE! Why not let this lady have the peace of mind to have her system checked out? Why not??? I've been working on HWH systems for over 15 years and I've done my fair share of - sounds like and feels like and might be's over the phone. But unless i know for sure what's going on, when gas and fire and water are involved, I don't say what's wrong or what NOT to worry about. It's all advice given under advisement. How can you be so sure!
Yes, this does sound like a condensation problem. Cold water may possibly be entering the tank, and is cooling, whereas the combustion gases cool to the point that water from the flue gases condenses, but I CAN'T say for sure. If you want to get some reliable info, go to www.plumbingnet.com and click your way around to find the phone # of the mfgr. of your unit, and call them since the installer / dealer won't help you. Read the make and model info on the label exernal to the tank.
The problem could also be caused by an insufficient flame which allows the combustion chamber to be cooled too low, below its condensation point. This would be an equipment problem most likely covered by the Tank's warrenty. If nothing else works out - you might try increasing the HW Tank's temperature set point.