Chris, thanks for testing on your end. I may not have been entirely clear in my explanation of the problem. Looks like you did not flag the output of your Merge tool as a parameter, so it's not surprising that it doesn't show up in the model tool dialog when running the model as a tool. I on the other hand intentionally specified the output of my Merge tool to be a parameter and also marked to "Add To Display", because I wanted to add the feature class to the ArcMap TOC, and I'm unaware of any other way to make data layers from models display in the TOC other than by making them parameters.
To clarify, what I'm questioning is why the feature class that is output from the Merge tool is considered by ModelBuilder to be an Input, Required parameter rather than an Output, Derived parameter. I'd prefer the parameter to not show up in the model tool dialog. The only way I can see to make it not show up there is to make the parameter "Managed", which disables my ability to name the FC something more user friendly. Perhaps this behavior is by design and there is no way to have the model both 1) not display the parameter in the tool dialog and 2) still allow me to name it what I want?