It is change any fuel type such as gas to oil or back. Not applicable in your case but I included it as FYI because these threads are an educational experience for all here.
Again, the mfr.s ASSumption is a properly constructed clay lined chimney that is still intact and in good shape. What I'm saying is, a professional inspection will most likely reveal defects in the flue such as damaged flue tiles, missing mortar, etc. that, according to code, require the chimney be relined. If you take your point literally, you could attach a combustion appliance to any old chimney that has some terra cotta flue tiles located inside it and you think it would be acceptable. Well, the code happens to disagree with this position. Now, since you are going from a draft hood appliance to a fan assisted one (if you choose 80% chimney vented option) then an internal inspection of the chimney (read-Level II) is triggered and the chimney must be suitable for the class of service.
All mfrs say clay flue lined chimneys are acceptable but most are weak on the details of what is an acceptable chimney. Why? Because they want to sell product. If you read elsewhere those mfrs. instructions should also mention install to the local codes. That brings in your State and/ or local building codes, which also bring in other industry stds., such as NFPA 211, which is where the level II inspection can be found. Yes, a WH can be common vented legally IF the chimney is suitable and not oversized. What I mentioned was outside of the code but a function issue that a legally vented WH and 80% furnace can be a hazard but there is a way to minimize the risk.
The problem with an orphaned WH is it cannot vent properly in what has become an oversized cold wet flue. Take your typical 40,000 BTU gas WH venting by itself into a nominal 8x8 tile flue. Where before you had the additional heat of a common vented furnace to warm and dry the flue, you don't anymore. If you figure the WH is roughly 75% efficient that means about 10,000 BTU/hr are lost up the stack when firing. This is not enough energy to dry the condense moisture off the face of most flue tiles let alone warm the surface of the flue so you can establish a draft and vent up the chimney. What often happens is instead, with the chimney full of a plug of cold dense air, it backdrafts out the draft hood into the building. When you inspect the chimney flue you may not see damage and assume everything is ok.
A thin-walled metallic liner has very low mass so it dries quickly, heats up quickly and can establish a draft within a few seconds rather than minutes. It contains the water vapor so you don't get condensation wicking out the mortar joints into the building were it can damage walls and ceilings.
A masonry chimney is just that--constructed or brick, mortar, stone or similar materials. It must be lined (since 1927) with a 1" clearance to combustibles for exterior chimneys/ 2" for interior chimneys. The approved liners may be a terra cotta tile that meets ASTM C-315 with a medium duty non-water soluble calcium aluminate refractory cement mixture mortar laid thin and struck smooth inside the flue or you may use a listed liner. Otherwise, you may use a listed vent such as B-vent listed to UL 441, L-vent (designed for oil but approved for CAT I gas) listed to UL 641, a factory chimney listed to UL 103 (does not require the HT high temperature designation as woodstoves do) or a liner listed to UL 1777. Some municipalities still approved of flues lined with firebrick and refractory mortar but those are all but gone. All listed products must be installed in accordance with their listed instructions. You must check local codes because if a local code exceeds the listing then the more restrictive requirement prevails. A common example of this is where a mfr. approves sidewall venting 12" above grade and the snow line but the State requires 4 feet above snow with a sign stating do not allow snow to block the gas vent.