As I understand it, this is incorrect. According to AN:This is because City2 really has a threshold of X-4+6 so it will always be higher if we are going by improvements. The X threshold is being determined by City1(Upper Valleyhome in this case).
I may have screwed up the math a bit, but the default threshold for Valleyhome is 20, then for Sacred forest is 4 lower, so 16. Valleyhome goes up to 25 with its specials, so Sacred Forest is 4 lower, 21, but then it goes up again for walls and aqueduct to 23.
This tells us that the base threshold of City3 is the threshold of City2 - 5 after factoring in all of City2's infrastructure. This should mean that, assuming they can both build all the same buildings, City2 cannot match the maximum threshold of City3.