Thanks for clarifying, Joshua.
I did some tests and found that both "date" and "timestamp" run successfully in the Make Query Table tool. However, only the word "timestamp" auto-completes in blue in the SQL query dialog box; "date" does not. I'm not sure why, but it must have some indication of what's going on behind the scenes in the software.
Dragging the tool history into Model Builder also runs fine inside Model Builder, with no warnings, in Clause and SQL query modes.
However, when I save the model and open it as a GP Tool, I get an error saying "Internal Error initializing expression."
If I try to switch from SQL to Clause mode, I get a warning that "the source layer or table is not valid". This is with the input layer hard-coded into the tool, not set as a parameter.
This definitely backs up your assertion that this is a combination Model Builder / Make Query Table error, and has nothing to do with the data type keyword.