Yes, the link works in my browser, I failed to mention that. I've cleared my cache to double check I'm not looking at a cached version on my browser. I have checked that the string I am inputting into get is correct, too. None of the file names have spaces or any other characters that require escapes.
Okay, new discovery: I can get files with question marks in the path from other websites, for example this node. Starting to think it likely has nothing to do with the URL (URI? My terminology is a bit hazy) and has everything to do with the particular website I am trying to access. Maybe it is blocking access from non-browsers. I should probably pursue this internally now, thank you for the help.