First off - if the house was constructed correctly, even 100 years ago, there would be separate flues for the fireplace and the water heater / furnace in the masonry chimney. The wood fireplace will have one flue in the brick chimney dedicated to it. The furnace and the water tank will share the other flue.
The fireplace would not necessarily have a liner. (It doesn't need one if it's an open fireplace.) It may at the very top have a clay liner sticking out and that is fine.
The flue assembly you describe is I believe a conventional vent set up. You have a metal flue coming off of the water tank and a metal flue coming off of the furnace and they join together BEFORE they exit the foundation wall in what is called a "Y Tee assembly". (In other words, both metal flues join together and meld into 1 pipe which then goes through the foundation wall and up the chimney.)
All natural gas appliances must have chimney liners. This is mandated by the Natural Gas Code (not the building code -sigh) Chimney liners are required because when natural gas combusts one of the byproducts of combustion is water in vapour form (the other being CO2 and CO). If you have a brick chimney without a liner, the water vapour will penetrate the brick and the mortar of the masonry chimney, then in the winter months, it will freeze, expand and blow apart the structure of your chimney.
Chimney liners are usually stainless steel.
Chimney liners MUST MUST MUST be properly sized according to the BTUs of the appliances feeding into them. A chimney liner that is too big is just as bad as one that is too small.
You cannot buy a chimney liner even if you wanted to without your Gas Fitter's ticket.
The tech was not scamming you.
If you are exhausting through a metal pipe up a masonry chimney, you definitely need a chimney liner.
The above picture shows a typical masonry chimney where you can clearly see that the flue on the left is a completely separate flue and exhausts a woodburning fireplace. The flue on the right is properly linered and exhausts a conventional furnace and hot water tank.