This type of problem is exactly the sort of reason I've been hesitant to invest in cloud-based services like this. I've always preferred buying my own own music to something like Spotify, but when Apple Music came out, I thought I'd give it a shot because it seemed to integrated and seamless. Now, however, I find myself completely unable to access any of the music that I've added to my library in iTunes on my Mac through Apple Music because I hadn't bothered to make them available offline.
Sure this is temporary, and it's really a first-world problem to complain about not having access to a nearly unlimited library of music for a few hours or whatnot, but it realizes my fears about the service and makes me think twice about keeping it once the trial ends.
I think what makes this worse, though, is ironically that it IS so integrated. If I subscribed to Spotify and it went down for a while, it would be entirely clear to me which things I could and couldn't play. I just wouldn't bother opening Spotify until it was fixed. I'd to open iTunes or the Music app on my phone and play the local content. Instead, I'm greeted with cloud icons on my Mac, or grayed out items on my phone.