Leaking pipe or toilet?

I had a plumber in to evaluate a leak in our waste line below one of our toilets. Work has not begun. The leak is in the basement. The basement is partially finished, so there is a ceiling under the rafters. But it is already cut away in the area of the leak, leak has not damage the ceiling. Uncertain about the floor below the toilet.
The leak was falling onto smaller pipes below, which confused me at first. But I eventually saw the leak dropping from higher, and the leak has been discoloured.

The leak only happens during and immediately after a flush of that toilet.

I had assumed the leak was in the pipe. But I can't see that.
The house is 80 years old, the toilet is not that old. The bathroom floor has multiple layers of remodeling. The top most level is tile about .3 - .5 inch thick. If the leak were just under the toilet, it could be obstructed by the raised floor.

The plumber wants to replace the toilet.

Could someone explain to me how the actual toilet could be at fault? This is going through a home warranty company, and I really don't feel like I am the plumbers customer. The plumber looked at the toilet and looked in the ceiling hole. He never flushed the toilet or saw the leak in action.

I wouldn't trust him if he never mentioned why it needed to be replaced.
If he said there was a crack in it somewhere, then yeah, it would have to be replaced.

Chances are it just needs a new seal and/or that the toilet flange that sits on top of the pipe may not be high enough.
If that's the case, they have various types of extensions or spacers that can be used. In fact, I'm sure one of the experienced plumbers here with have more specific recommendations, if you were going to do it yourself.

CALL ANOTHER PLUMBER!

You could call and ask him why it needs to be replaced, then CALL ANOTHER PLUMBER!

Home warranty companies sometimes hire the cheapest knucklehead they can find.

You can call the home warranty company, and tell them the first plumber is apparently incompetent.
You can demand a different plumber.

The problem is most likely an old damaged flange, or as suggested above me the flange is too low in the layers of flooring.
Or the flooring is soft from years of slow leaks, and so the toilet is not maintaining its position tight against the wax sealing ring.