You might be on to something here. As I was trying out all the different apps this morning, I happen to choose to play Beastie Boys Paul Revere and it played. I tried another song but got the same error mentioned about about the song being sideloaded. After reading through the thread, I looked and Paul Revere is not on my SD card but I must have uploaded it to the cloud back when I had the GNEX.
I almost exclusively use Power Amp as my music player to play songs loaded on my SD card.
I doubt you will see the option of which music you want played as this is Google's plan to move everything to the cloud as seen by no SD cards in their Nexus devices, the new Droid phones and the new Moto X phone.
For me, I prefer having the SD slot but if they want me to move to the cloud, no problem and Verizon will have to pull my unlimited plan from my dead hands!
EDIT: Just remembered, Chromecast was setup to pull from the cloud so unless Google provides a way for 3rd party devs to allow streaming from your SD card, I don't think it's going to happen.
There is a setting in Google Play Music that selects "All Music" or "On Device" music, you may want to check that. My Chromecast is sitting in a box at my front door at the moment...so this is just a guess on how to tackle your problem.