Well, I'm a bit confused, so please, bear with me:
I have a Pi3 with Raspbian (huh, the latest one, can't remember the name) and an external HDD plugged to it. I've been doing tests and reading stuff, and noticed that I didn't really needed to run the desktop environment for the stuff I was using the pi, so I went sudo raspi-config and removed it (Boot Options -> Desktop/CLI -> Console Autologin) .
Now, for the record, this is the ls -l on the /media/pi folder before:
drwxr-xr-x 7 root root 4096 may 9 2014 RaspberryData
On reboot, I got a prompt telling me that "access denied". The ls -l is this:
drwx------ 2 root root 4096 oct 22 22:04 RaspberryData
Reading a bit, its telling me that when there's no Desktop, neither the "groups" triplet nor the "other" triplet don't have access. I guess the main problem is with the "groups" triplet, as with the Pixel environment I could read and execute stuff.
Now, I guess this could go with a chown on the folder/mountpoint, but before doing anything I would like to know the whys and hows, and if I'm mistaken, the whats (Then the whys and finally the hows).