Not true, and easily proven so. Hell, the game I was just playing had numerous instances of this. Assuming the industrial sector is completely constructed, upgrading to a CIC costs 6 bc, or one turn of construction (assuming at least 1 MP). Building the CIC from scratch might take 30+ turns depending on MP available, or cost ~3200 bc to buy.
I didn't test every single improvement over every other improvement.
In particular, it seems I tested primarily (if not entirely) early game improvements.
Which would explain it, actually.
All the early game improvements cost 50 production or less, so I wasn't seeing any significant difference in production between them. The upgrade cost is assumed to be 50 instead (in most of the examples I ran), therefore you don't actually save any money, time, or production by building over them with an "equivalent".
And I just now noticed this by attempting to build an embassy over a traditional factory (which would cost me 50) versus building an embassy on bare ground (which would cost me 30).
So you have new building cost minus initial building cost (actually if rush buying is any indicator it uses the total social production spent on it, not the cost), but if the new building is actually cheaper than the initial building, then you pay 50 production to upgrade it.
I apologize for not being more thorough.