Ex: New baseplate/new file that hasn’t been uploaded to Roblox.
Without uploading:
After uploading:

If I create a basic animation, upload it to the website, and then add a script to run the animation, it works fine. Are you using a different process to use animations? What OS are you using?
Place file is the exact same, I uploaded it directly after I took the first screenshot.
Operating System is Windows 8.1
“http://assetgame.roblox.com/asset/?id=364545144&serverplaceid=95206881”
That placeid leads to Baseplate - Roblox.
That place (owner) doesn’t have access to your animations, so you can’t load them in studio.
If you want a baseplate in studio, press the “New” (ctrl+N) icon.
That way, the placeid is 0, so the limitations don’t apply.
TL;DR: New File ~= Baseplate template
Thanks for the repro solution! I’ll add that one to our bug list.