Yes, your explanation is correct. The “Design Water Temperature” property does not really affect the temperatures experienced in the simulation. It is just a property of what the system is designed to handle and not how it actually ends up functioning at over the course of a year. So you can build a system to handle temperatures of 82C water but you actually operate it at 50C. Changing the “Design Water Temperature” may affect some curves used to describe some of the HVAC equipment but, unless to change it to a totally nonsensical value, I have usually found that it does not affect the simulation in a noticeable way.
BTW, you can always verify that the supply temperatures are what you expect by requesting node-level temperature results from a simulation like so:
Typically, HVAC systems have a lot of nodes (even when it is only serving a single zone) so be prepared to import a lot of data into Grasshopper if you do this. Also, to make sure that you are looking at the right part of the HVAC system, you probably want to open the .osm in OpenStudio, go to the HVAC tab, and click on some of the different nodes to make sure you select the right node number from the data tree of all temperatures that you get when you request node-level results.