Probably the calcium buildup he was referring to was in the holes or passages under the rim. These areas definitely do get limed up, and that for sure can affect bowl washdown and the rim flush action. You also get a scale buildup in the throat and trapway. This is not a buildup such that it blocks the pipes, but it adds a lot of friction, and for sure this also affects flushing. This is why reputable manufacturers take the extra step of completely glazing the waterways and trapways.
The fact the your new toilet is performing well seems to confirm the diagnosis on the old toilet.