For the sake of completeness here is the solution: I reached out for the iA Writer support and they gave me the following hints:
While support for scripting falls a bit outside our scope of support, it sounds like this is a sandboxing issue.
If the folder containing the file is added to iA Writer's Library, you will likely not see this when attempting to launch your file since iA Writer will have the necessary permissions to access the file.
Alternatively, you might be able to accomplish your intended task by using instead a shell script in Apple Script. For example, something like this for your test file:
do shell script "open /Users/jbedenbender/test.md -a \"iA Writer\""
The first solution worked out for me, but I think there will be times when the second one becomes handy.