The reality is that Ludwig's dad Max II was not involved in the construction of this castle. He purchased it intact. In fact, it possibly dates as far back as the 14th century (not 100% clear as the records are not great and apparently this castle had a different name before the 19th century, and it's not always clear whether the name Hohenschwangau is referring to this castle in records, or to another castle it swapped names with)